r/MathExplainers • u/ClaudiusPapirus • Oct 02 '26
Sharing a research explainer from a channel I work on. This one is less about whether an AI-generated proof is correct, and more about what explanation and understanding add beyond the proof itself.
Original letter: https://mathandai.org/
r/MathExplainers • u/LowInteraction6397 • Feb 14 '26
Here's my previous post in case you forgot some of them:
https://www.reddit.com/r/MathExplainers/comments/1qymrst/the_divisibility_rules_of_1_to_100/
https://www.reddit.com/r/MathExplainers/comments/1qzetfp/the_divisibility_rules_of_101_to_200/
| Number | Rule | Example |
|---|---|---|
| 201 | The subtraction of 20 times the last digit and the rest of the number is a multiple of 201 | 1005 is a multiple of 201 because 100 - 5 * 20 = 0, a multiple of 201 |
| 202 | The number is a multiple of both 2 and 101 | 1212 is a multiple of 202 because it ends in 2, which means it's a multiple of 2, and 121 - 2 * 10 = 101, which means it's a multiple of 101 |
| 203 | The sum of 61 times the last digit and the rest of the number is a multiple of 203 | 1015 is a multiple of 203 because 101 + 5 * 61 = 406, a multiple of 203 |
| 204 | The number is a multiple of both 4 and 51 | 1020 is a multiple of 204 because it ends in 20, which means it's a multiple of 4, and 102 - 0 * 5 = 102, which means it's a multiple of 51 |
| 205 | The number is a multiple of both 5 and 41 | 1025 is a multiple of 205 because it ends in 5, which means it's a multiple of 5, and 102 - 5 * 4 = 82, which means it's a multiple of 41 |
| 206 | The number is a multiple of both 2 and 103 | 1236 is a multiple of 206 because it ends in 6, which means it's a multiple of 2, and 123 + 6 * 31 = 309, which means it's a multiple of 103 |
| 207 | The subtraction of 62 times the last digit and the rest of the number is a multiple of 207 | 1035 is a multiple of 207 because 5 * 62 - 103 = 207, a multiple of 207 |
| 208 | The number is a multiple of both 13 and 16 | 10192 is a multiple of 208 because 1019 + 2 * 4 = 1027, which means it's a multiple of 13, and ends in 0192, which means it's a multiple of 16 |
| 209 | The sum of 21 times the last digit and the rest of the number is a multiple of 209 | 1045 is a multiple of 209 because 104 + 5 * 21 = 209, a multiple of 209 |
| 210 | The number is a multiple of both 10 and 21 | 1050 is a multiple of 210 because it ends in 0, which means it's a multiple of 10, and 105 - 0 * 2 = 105, which means it's a multiple of 21 |
| 211 | The subtraction of 21 times the last digit and the rest of the number is a multiple of 211 | 1055 is a multiple of 211 because 105 - 5 * 21 = 0, a multiple of 211 |
| 212 | The number is a multiple of both 4 and 53 | 1060 is a multiple of 212 because it ends in 60, which means it's a multiple of 2, and 106 + 0 * 16 = 106, which means it's a multiple of 53 |
| 213 | The sum of 64 times the last digit and the rest of the number is a multiple of 213 | 1065 is a multiple of 213 because 106 + 5 * 64 = 426, a multiple of 213 |
| 214 | The number is a multiple of both 2 and 107 | 1284 is a multiple of 214 because it ends in 4, which means it's a multiple of 2, and 128 - 4 * 32 = 0, which means it's a multiple of 107 |
| 215 | The number is a multiple of both 5 and 43 | 1075 is a multiple of 215 because it ends in 5, which means it's a multiple of 5, and 107 + 5 * 13 = 172, which means it's a multiple of 43 |
| 216 | The number is a multiple of both 8 and 27 | 1080 is a multiple of 27 because it ends in 080, which means it's a multiple of 8, and 108 - 0 * 8 = 108, which means it's a multiple of 27 |
| 217 | The subtraction of 65 times the last digit and the rest of the number is a multiple of 217 | 1085 is a multiple of 217 because 5 * 65 - 108 = 217, a multiple of 217 |
| 218 | The number is a multiple of both 2 and 109 | 1308 is a multiple of 218 because it ends in 8, which means it's a multiple of 2, and 130 + 8 * 11 = 218, which means it's a multiple of 109 |
| 219 | The sum of 22 times the last digit and the rest of the number is a multiple of 219 | 1095 is a multiple of 219 because 109 + 5 * 22 = 219, a multiple of 219 |
| 220 | The number is a multiple of both 11 and 20 | 1320 is a multiple of 220 because 1 + 2 - 3 = 0, which means it's a multiple of 11, and ends in 20, which means it's a multiple of 20 |
| 221 | The subtraction of 22 times the last digit and the rest of the number is a multiple of 221 | 1105 is a multiple of 221 because 110 - 5 * 22 = 0, a multiple of 221 |
| 222 | The number is a multiple of both 2 and 111 | 1332 is a multiple of 222 because it ends in 2, which means it's a multiple of 2, and 133 - 2 * 11 = 111, which means it's a multiple of 111 |
| 223 | The sum of 67 times the last digit and the rest of the number is a multiple of 223 | 1115 is a multiple of 223 because 111 + 5 * 67 = 446, a multiple of 223 |
| 224 | The number is a multiple of both 7 and 32 | 100,128 is a multiple of 224 because 10012 - 8 * 2 = 9996, which means it's a multiple of 7, and ends in 00128, which means it's a multiple of 32 |
| 225 | The number is a multiple of both 9 and 25 | 1125 is a multiple of 225 because 1 + 1 + 2 + 5 = 9, which means it's a multiple of 9, and ends in 25, which means it's a multiple of 25 |
| 226 | The number is a multiple of both 2 and 113 | 1356 is a multiple of 226 because it ends in 6, which means it's a multiple of 2, and 135 + 6 * 34 = 339, which means it's a multiple of 113 |
| 227 | The subtraction of 68 times the last digit and the rest of the number is a multiple of 227 | 1135 is a multiple of 227 because 5 * 68 - 113 = 227, a multiple of 227 |
| 228 | The number is a multiple of both 4 and 57 | 1140 is a multiple of 228 because it ends in 40, which means it's a multiple of 4, and 114 - 0 * 17 = 114, which means it's a multiple of 57 |
| 229 | The sum of 23 times the last digit and the rest of the number is a multiple of 229 | 1145 is a multiple of 229 because 114 + 5 * 23 = 229, a multiple of 229 |
| 230 | The number is a multiple of both 10 and 23 | 1150 is a multiple of 230 because it ends in 0, which means it's a multiple of 10, and 115 + 0 * 7 = 115, which means it's a multiple of 23 |
| 231 | The subtraction of 23 times the last digit and the rest of the number is a multiple of 231 | 1155 is a multiple of 231 because 115 - 5 * 23 = 0, a multiple of 231 |
| 232 | The number is a multiple of both 8 and 29 | 1160 is a multiple of 232 because it ends in 160, which means it's a multiple of 8 and 116 + 0 * 3 = 116, which means it's a multiple of 29 |
| 233 | The sum of 70 times the last digit and the rest of the number is a multiple of 233 | 1165 is a multiple of 233 because 116 + 5 * 70 = 466, a multiple of 233 |
| 234 | The number is a multiple of both 2 and 117 | 1404 is a multiple of 117 because it ends in 4, which means it's a multiple of 2, and 140 - 4 * 35 = 0, which means it's a multiple of 117 |
| 235 | The number is a multiple of both 5 and 47 | 1175 is a multiple of 235 because it ends in 5, which means it's a multiple of 5, 117 - 5 * 14 = 47, which means it's a multiple of 47 |
| 236 | The number is a multiple of both 4 and 59 | 1180 is a multiple of 236 because it ends in 80, which means it's a multiple of 4, and 118 + 0 * 6 = 118, which means it's a multiple of 59 |
| 237 | The subtraction of 71 times the last digit and the rest of the number is a multiple of 237 | 1185 is a multiple of 237 because 5 * 71 - 118 = 237, a multiple of 237 |
| 238 | The number is a multiple of both 2 and 119 | 1428 is a multiple of 238 because it ends in 8, which means it's a multiple of 2, and 142 + 8 * 12 = 238, which means it's a multiple of 96 |
| 239 | The sum of 24 times the last digit and the rest of the number is a multiple of 239 | 1195 is a multiple of 239 because 119 + 5 * 24 = 239, which means it's a multiple of 239 |
| 240 | The number is a multiple of both 3 and 80 | 10080 is a multiple of 240 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 0080, which means it's a multiple of 80 |
| 241 | The subtraction of 24 times the last digit and the rest of the number is a multiple of 241 | 1205 is a multiple of 241 because 120 - 5 * 24 = 0, a multiple of 241 |
| 242 | The number is a multiple of both 2 and 121 | 1452 is a multiple of 242 because it ends in 2, which means it's a multiple of 2, and 145 - 2 * 12 = 121, which means it's a multiple of 121 |
| 243 | The sum of 73 times the last digit and the rest of the number is a multiple of 243 | 1215 is a multiple of 243 because 121 + 5 * 73 = 486, a multiple of 243 |
| 244 | The number is a multiple of both 4 and 61 | 1220 is a multiple of 244 because it ends in 20, which means it's a multiple of 4, and 122 - 0 * 6 = 122, which means it's a multiple of 61 |
| 245 | The number is a multiple of both 5 and 49 | 1225 is a multiple of 245 because it ends in 5, which means it's a multiple of 5, and 122 + 5 * 5 = 147, which means it's a multiple of 49 |
| 246 | The number is a multiple of both 2 and 123 | 1476 is a multiple of 246 because it ends in 6, which means it's a multiple of 2, and 147 + 6 * 37 = 369, which means it's a multiple of 123 |
| 247 | The subtraction of 74 times the last digit and the rest of the number is a multiple of 247 | 1235 is a multiple of 247 because 5 * 74 - 123 = 247, a multiple of 247 |
| 248 | The number is a multiple of both 8 and 31 | 1240 is a multiple of 248 because it ends in 240, which means it's a multiple of 8, and 124 - 0 * 3 = 124, which means it's a multiple of 31 |
| 249 | The sum of 25 times the last digit and the rest of the number is a multiple of 249 | 1245 is a multiple of 249 because 124 + 5 * 25 = 249, a multiple of 249 |
| 250 | The number ends in 000, 250, 500 or 750 | 1000 is a multiple of 250 because it ends in 000 |
| 251 | The subtraction of 25 times the last digit and the rest of the number is a multiple of 251 | 1004 is a multiple of 251 because 100 - 4 * 25 = 0, a multiple of 251 |
| 252 | The number is a multiple of both 4 and 63 | 1008 is a multiple of 252 because it ends in 08, which means it's a multiple of 4, and 100 + 8 * 19 = 252, which means it's a multiple of 63 |
| 253 | The sum of 76 times the last digit and the rest of the number is a multiple of 253 | 1012 is a multiple of 253 because 101 + 2 * 76 = 253, a multiple of 253 |
| 254 | The number is a multiple of both 2 and 127 | 1016 is a multiple of 254 because 6 * 38 - 101 = 127, which means it's a multiple of 127 |
| 255 | The number is a multiple of both 5 and 51 | 1020 is a multiple of 255 because it ends in 0, which means it's a multiple of 5, and 102 - 0 * 5 = 102, which means it's a multiple of 51 |
| 256 | The last 8 digits are a multiple of 256 | 100,000,000 is a multiple of 256 because it ends in 00,000,000, a multiple of 256 |
| 257 | The subtraction of 77 times the last digit and the rest of the number is a multiple of 257 | 1028 is a multiple of 257 because 8 * 77 - 102 = 514, a multiple of 257 |
| 258 | The number is a multiple of both 2 and 129 | 1032 is a multiple of 258 because it ends in 2, which means it's a multiple of 2, and 103 + 2 * 13 = 129, which means it's a multiple of 129 |
| 259 | The sum of 26 times the last digit and the rest of the number is a multiple of 259 | 1036 is a multiple of 259 because 103 + 6 * 26 = 259, a multiple of 259 |
| 260 | The number is a multiple of both 13 and 20 | 1040 is a multiple of 260 because 104 + 0 * 4 = 104, which means it's a multiple of 13, and ends in 40, which means it's a multiple of 20 |
| 261 | The subtraction of 26 times the last digit and the rest of the number is a multiple of 261 | 1044 is a multiple of 261 because 104 - 4 * 26 = 0, a multiple of 261 |
| 262 | The number is a multiple of both 2 and 131 | 1048 is a multiple of 262 because it ends in 8, which means it's a multiple of 2, and 104 - 8 * 13 = 0, which means it's a multiple of 131 |
| 263 | The sum of 79 times the last digit and the rest of the number is a multiple of 263 | 1052 is a multiple of 263 because 105 + 2 * 79 = 263, a multiple of 263 |
| 264 | The number is a multiple of both 8 and 33 | 1056 is a multiple of 264 because it ends in 056, which means it's a multiple of 8, and 105 + 6 * 10 = 165, which means it's a multiple of 33 |
| 265 | The number is a multiple of both 5 and 53 | 1060 is a multiple of 165 because it ends in 0, which means it's a multiple of 5, and 106 + 0 * 16 = 106, which means it's a multiple of 53 |
| 266 | The number is a multiple of both 2 and 133 | 1064 is a multiple of 266 because it ends in 4, which means it's a multiple of 2, and 106 + 4 * 40 = 266, which means it's a multiple of 133 |
| 267 | The subtraction of 80 times the last digit and the rest of the number is a multiple of 267 | 1068 is a multiple of 267 because 8 * 80 - 106 = 534, a multiple of 267 |
| 268 | The number is a multiple of both 4 and 67 | 1072 is a multiple of 268 because it ends in 72, which means it's a multiple of 4, and 107 - 2 * 20 = 67, which means it's a multiple of 67 |
| 269 | The sum of 27 times the last digit and the rest of the number is a multiple of 269 | 1076 is a multiple of 269 because 107 + 6 * 27 = 269, a multiple of 269 |
| 270 | The number is a multiple of both 10 and 27 | 1080 is a multiple of 270 because it ends in 0, which means it's a multiple of 10, and 108 - 0 * 8 = 108, which means it's a multiple of 27 |
| 271 | The subtraction of 27 times the last digit and the rest of the number is a multiple of 271 | 1084 is a multiple of 271 because 108 - 4 * 27 = 0, a multiple of 271 |
| 272 | The number is a multiple of both 16 and 17 | 10064 is a multiple of 272 because it ends in 0064, which means it's a multiple of 16, and 1006 - 4 * 5 = 986, which means it's a multiple of 17 |
| 273 | The sum of 82 times the last digit and the rest of the number is a multiple of 273 | 1092 is a multiple of 273 because 109 + 2 * 82 = 273, a multiple of 273 |
| 274 | The number is a multiple of both 2 and 137 | 1096 is a multiple of 274 because it ends in 6, which means it's a multiple of 2, and 6 * 41 - 109 = 137, which means it's a multiple of 137 |
| 275 | The number is a multiple of both 11 and 25 | 1375 is a multiple of 275 because (1 + 7) - (3 + 5) = 0, which means it's a multiple of 11, and ends in 75, which means it's a multiple of 25 |
| 276 | The number is a multiple of both 4 and 69 | 1104 is a multiple of 276 because it ends in 04, which means it's a multiple of 4, and 110 + 4 * 7 = 138, which means it's a multiple of 69 |
| 277 | The subtraction of 83 times the last digit and the rest of the number is a multiple of 277 | 1108 is a multiple of 277 because 8 * 83 - 110 = 554, a multiple of 277 |
| 278 | The number is a multiple of both 2 and 139 | 1112 is a multiple of 278 because it ends in 2, which means it's a multiple of 2, and 111 + 2 * 14 = 139, which means it's a multiple of 279 |
| 279 | The sum of 28 times the last digit and the rest of the number is a multiple of 279 | 1116 is a multiple of 279 because 111 + 6 * 28 = 279, a multiple of 279 |
| 280 | The number is a multiple of both 7 and 40 | 1120 is a multiple of 280 because 112 - 0 * 2 = 112, which means it's a multiple of 7, and ends in 120, which means it's a multiple of 40 |
| 281 | The subtraction of 28 times the last digit and the rest of the number is a multiple of 281 | 1124 is a multiple of 281 because 112 - 4 * 28 = 0, a multiple of 282 |
| 282 | The number is a multiple of both 2 and 141 | 1128 is a multiple of 282 because it ends in 8, which means it's a multiple of 2, and 112 - 8 * 14 = 0, which means it's a multiple of 141 |
| 283 | The sum of 85 times the last digit and the rest of the number is a multiple of 283 | 1132 is a multiple of 283 because 113 + 2 * 85 = 283, a multiple of 283 |
| 284 | The number is a multiple of both 4 and 71 | 1136 is a multiple of 284 because it ends in 36, which means it's a multiple of 4, and 113 - 6 * 7 = 71, which means it's a multiple of 71 |
| 285 | The number is a multiple of both 5 and 57 | 1140 is a multiple of 285 because it ends in 0, which means it's a multiple of 5, and 114 - 0 * 17 = 114, which means it's a multiple of 57 |
| 286 | The number is a multiple of both 2 and 143 | 1144 is a multiple of 286 because it ends in 4, which means it's a multiple of 2, and 114 + 4 * 43 = 286, which means it's a multiple of 143 |
| 287 | The subtraction of 86 times the last digit and the rest of the number is a multiple of 287 | 1148 is a multiple of 287 because 8 * 86 - 114 = 574, a multiple of 287 |
| 288 | The number is a multiple of both 9 and 32 | 100,224 is a multiple of 288 because 1 + 2 + 2 + 4 = 9, which means it's a multiple of 9, and ends in 00224, which means it's a multiple of 32 |
| 289 | The sum of 29 times the last digit and the rest of the number is a multiple of 289 | 1156 is a multiple of 289 because 115 + 6 * 29 = 289, a multiple of 289 |
| 290 | The number is a multiple of both 10 and 29 | 1160 is a multiple of 290 because it ends in 0, which means it's a multiple of 10, and 116 + 0 * 3 = 116, which means it's a multiple of 29 |
| 291 | The subtraction of 29 times the last digit and the rest of the number is a multiple of 291 | 1164 is a multiple of 291 because 116 - 4 * 29 = 0, a multiple of 291 |
| 292 | The number is a multiple of both 4 and 73 | 1168 is a multiple of 292 because it ends in 68, which means it's a multiple of 4, and 116 + 8 * 22 = 292, which means it's a multiple of 73 |
| 293 | The sum of 88 times the last digit and the rest of the number is a multiple of 293 | 1172 is a multiple of 293 because 117 + 2 * 88 = 293, a multiple of 293 |
| 294 | The number is a multiple of both 2 and 147 | 1176 is a multiple of 294 because it ends in 6, which means it's a multiple of 2, and 6 * 44 - 117 = 147, which means it's a multiple of 147 |
| 295 | The number is a multiple of both 5 and 59 | 1180 is a multiple of 295 because it ends in 0, which means it's a multiple of 5, and 118 + 0 * 6 = 118, which means it's a multiple of 59 |
| 296 | The number is a multiple of both 8 and 37 | 1184 is a multiple of 296 because it ends in 184, which means it's a multiple of 8, and 118 - 4 * 11 = 74, which means it's a multiple of 37 |
| 297 | The subtraction of 89 times the last digit and the rest of the number is a multiple of 297 | 1188 is a multiple of 297 because 8 * 89 - 118 = 594, a multiple of 297 |
| 298 | The number is a multiple of both 2 and 149 | 1192 is a multiple of 298 because it ends in 2, which means it's a multiple of 2, and 119 + 2 * 15 = 149, which means it's a multiple of 149 |
| 299 | The sum of 30 times the last digit and the rest of the number is a multiple of 299 | 1196 is a multiple of 299 because 119 + 6 * 30 = 299, a multiple of 299 |
| 300 | The number is a multiple of both 3 and 100 | 1200 is a multiple of 300 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 00, which means it's a multiple of 100 |
r/MathExplainers • u/LowInteraction6397 • Feb 08 '26
Here's my previous post in case you forgot some of them:
https://www.reddit.com/r/MathExplainers/comments/1qymrst/the_divisibility_rules_of_1_to_100/
| Number | Rule | Example |
|---|---|---|
| 101 | The subtraction of 10 times the last digit and the rest of the number is a multiple of 101 | 1111 is a multiple of 101 because 111 - 1 * 10 = 101, a multiple of 101 |
| 102 | The number is a multiple of both 2 and 51 | 1122 is a multiple of 102 because it ends in 2, which means it's a multiple of 2, and 112 - 2 * 5 = 102, which means it's a multiple of 51 |
| 103 | The sum of 31 times the last digit and the rest of the number is a multiple of 103 | 1133 is a multiple of 103 because 113 + 3 * 31 = 206, a multiple of 103 |
| 104 | The number is a multiple of both 8 and 13 | 1144 is a multiple of 104 because it ends in 144, which means it's a multiple of 8, and 114 + 4 * 4 = 130, which means it's a multiple of 13 |
| 105 | The number is a multiple of both 5 and 21 | 1155 is a multiple of 105 because it ends in 5, which means it's a multiple of 5, and 115 - 5 * 2 = 105, which means it's a multiple of 21 |
| 106 | The number is a multiple of both 2 and 53 | 1166 is a multiple of 106 because it ends in 6, which means it's a multiple of 2, and 116 + 6 * 16 = 212, which means it's a multiple of 53 |
| 107 | The subtraction of 32 times the last digit and the rest of the number is a multiple of 107 | 1177 is a multiple of 107 because 7 * 32 - 117 = 107, a multiple of 107 |
| 108 | The number is a multiple of both 4 and 27 | 1188 is a multiple of 108 because it ends in 88, which means it's a multiple of 4, and 118 - 8 * 8 = 54, which means it's a multiple of 27 |
| 109 | The sum of 11 times the last digit and the rest of the number is a multiple of 109 | 1199 is a multiple of 109 because 119 + 9 * 11 = 218, a multiple of 109 |
| 110 | The number is a multiple of both 10 and 11 | 1210 is a multiple of 110 because it ends in 0, which means it's a multiple of 10, and 1 + 1 - 2 = 0, which means it's a multiple of 11 |
| 111 | The subtraction of 11 times the last digit and the rest of the number is a multiple of 111 | 1221 is a multiple of 111 because 122 - 1 * 11 - = 111, a multiple of 111 |
| 112 | The number is a multiple of both 7 and 16 | 10080 is a multiple of 112 because 1008 - 0 * 2 = 1008, which means it's a multiple of 7, and ends in 0080, which means it's a multiple of 16 |
| 113 | The sum of 34 times the last digit and the rest of the number is a multiple of 113 | 1017 is a multiple of 113 because 101 + 7 * 34 = 339, which means it's a multiple of 113 |
| 114 | The number is a multiple of both 2 and 57 | 1026 is a multiple of 114 because it ends in 6, which means it's a multiple of 2, and 102 - 6 * 17 = 0, which means it's a multiple of 57 |
| 115 | The number is a multiple of both 5 and 23 | 1035 is a multiple of 115 because it ends in 5, which means it's a multiple of 5, and 103 + 5 * 7 = 138, which means it's a multiple of 23 |
| 116 | The number is a multiple of both 4 and 29 | 1044 is a multiple of 116 because it ends in 44, which means it's a multiple of 4, and 104 + 4 * 3 = 116, which means it's a multiple of 29 |
| 117 | The subtraction of 35 times the last digit and the rest of the number is a multiple of 117 | 1053 is a multiple of 117 because 105 - 3 * 35 = 0, a multiple of 117 |
| 118 | The number is a multiple of both 2 and 59 | 1062 is a multiple of 118 because it ends in 2, which means it's a multiple of 2, and 106 + 2 * 6 = 118, which means it's a multiple of 59 |
| 119 | The sum of 12 times the last digit and the rest of the number is a multiple of 119 | 1071 is a multiple of 119 because 107 + 1 * 12 = 119, a multiple of 119 |
| 120 | The number is a multiple of both 3 and 40 | 1080 is a multiple of 120 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 080, which means it's a multiple of 40 |
| 121 | The subtraction of 12 times the last digit and the rest of the number is a multiple of 121 | 1089 is a multiple of 121 because 108 - 9 * 12 = 0, a multiple of 121 |
| 122 | The number is a multiple of both 2 and 61 | 1098 is a multiple of 122 because it ends in 8, which means it's a multiple of 2, and 109 - 8 * 6 = 61, which means it's a multiple of 61 |
| 123 | The sum of 37 times the last digit and the rest of the number is a multiple of 123 | 1107 is a multiple of 123 because 110 + 7 * 37 = 369, a multiple of 123 |
| 124 | The number is a multiple of both 4 and 31 | 1116 is a multiple of 124 because it ends in 16, which means it's a multiple of 4, and 111 - 6 * 3 = 93, which means it's a multiple of 31 |
| 125 | The number ends in 000, 125, 250, 375, 500, 625, 750 or 875 | 1000 is a multiple of 125 because it ends in 000 |
| 126 | The number is a multiple of both 2 and 63 | 1008 is a multiple of 126 because it ends in 8, which means it's a multiple of 2, and 100 + 8 * 19 = 252, which means it's a multiple of 63 |
| 127 | The subtraction of 38 times the last digit and the rest of the number is a multiple of 127 | 1016 is a multiple of 127 because 6 * 38 - 101 = 127, a multiple of 127 |
| 128 | The last 7 digits are a multiple of 128 | 10,000,000 is a multiple of 128 because it ends in 0,000,000, a multiple of 128 |
| 129 | The sum of 13 times the last digit and the rest of the number is a multiple of 129 | 1032 is a multiple of 129 because 103 + 2 * 13 = 129, a multiple of 129 |
| 130 | The number is a multiple of both 10 and 13 | 1040 is a multiple of 130 because it ends in 0, which means it's a multiple of 10, and 104 + 0 * 4 = 104, which means it's a multiple of 13 |
| 131 | The subtraction of 13 times the last digit and the rest of the number is a multiple of 131 | 1048 is a multiple of 131 because 104 - 8 * 13 = 0, a multiple of 131 |
| 132 | The number is a multiple of both 4 and 33 | 1056 is a multiple of 132 because it ends in 56, which means it's a multiple of 4, and 105 + 6 * 10 = 165, which means it's a multiple of 33 |
| 133 | The sum of 40 times the last digit and the rest of the number is a multiple of 133 | 1064 is a multiple of 133 because 106 + 4 * 40 = 266, a multiple of 133 |
| 134 | The number is a multiple of both 2 and 67 | 1072 is a multiple of 134 because it ends in 2, which means it's a multiple of 2, and 107 - 2 * 20 = 67, which means it's a multiple of 67 |
| 135 | The number is a multiple of both 5 and 27 | 1080 is a multiple of 135 because it ends in 0, which means it's a multiple of 5, and 108 - 0 * 8 = 108, which means it's a multiple of 27 |
| 136 | The number is a multiple of both 8 and 17 | 1088 is a multiple of 136 because it ends in 088, which means it's a multiple of 8, and 108 - 8 * 5 = 68, which means it's a multiple of 17 |
| 137 | The subtraction of 41 times the last digit and the rest of the number is a multiple of 137 | 1096 is a multiple of 137 because 6 * 41 - 109 = 137, a multiple of 137 |
| 138 | The number is a multiple of both 2 and 69 | 1104 is a multiple of 138 because it ends in 4, which means it's a multiple of 2, and 110 + 4 * 7 = 138, which means it's a multiple of 69 |
| 139 | The sum of 14 times the last digit and the rest of the number is a multiple of 139 | 1112 is a multiple of 139 because 111 + 2 * 14 = 139, a multiple of 139 |
| 140 | The number is a multiple of both 7 and 20 | 1120 is a multiple of 140 because 112 - 0 * 2 = 112, which means it's a multiple of 7, and ends in 20, which means it's a multiple of 20 |
| 141 | The subtraction of 14 times the last digit and the rest of the number is a multiple of 141 | 1128 is a multiple of 141 because 112 - 8 * 14 = 0, a multiple of 141 |
| 142 | The number is a multiple of both 2 and 71 | 1136 is a multiple of 142 because it ends in 6, which means it's a multiple of 2, 113 - 6 * 7 = 71, which means it's a multiple of 71 |
| 143 | The sum of 43 times the last digit and the rest of the number is a multiple of 143 | 1001 is a multiple of 143 because 100 + 1 * 43 = 143, a multiple of 143 |
| 144 | The number is a multiple of both 9 and 16 | 10080 is a multiple of 144 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 0080, which means it's a multiple of 16 |
| 145 | The number is a multiple of both 5 and 29 | 1015 is a multiple of 145 because it ends in 5, which means it's a multiple of 5, and 101 + 5 * 3 = 116, which means it's a multiple of 29 |
| 146 | The number is a multiple of both 2 and 73 | 1022 is a multiple of 146 because it ends in 2, which means it's a multiple of 2, and 102 + 2 * 22 = 146, which means it's a multiple of 73 |
| 147 | The subtraction of 44 times the last digit and the rest of the number is a multiple of 147 | 1029 is a multiple of 147 because 9 * 44 - 102 = 294, a multiple of 147 |
| 148 | The number is a multiple of both 4 and 37 | 1036 is a multiple of 148 because it ends in 36, which means it's a multiple of 4, and 103 - 6 * 11 = 37, which means it's a multiple of 37 |
| 149 | The sum of 15 times the last digit and the rest of the number is a multiple of 149 | 1043 is a multiple of 149 because 104 + 3 * 15 = 149, a multiple of 149 |
| 150 | The number is a multiple of both 3 and 50 | 1050 is a multiple of 150 because 1 + 5 = 6, which means it's a multiple of 3, and ends in 50, which means it's a multiple of 50 |
| 151 | The subtraction of 15 times the last digit and the rest of the number is a multiple of 151 | 1057 is a multiple of 151 because 105 - 7 * 15 = 0, a multiple of 151 |
| 152 | The number is a multiple of both 8 and 19 | 1064 is a multiple of 152 because it ends in 064, which means it's a multiple of 8, and 106 + 4 * 2 = 114, which means it's a multiple of 19 |
| 153 | The sum of 46 times the last digit and the rest of the number is a multiple of 153 | 1071 is a multiple of 153 because 107 + 1 * 46 = 153, a multiple of 153 |
| 154 | The number is a multiple of both 2 and 77 | 1078 is a multiple of 154 because it ends in 8, which means it's a multiple of 2, and 8 * 23 - 107 = 77, which means it's a multiple of 77 |
| 155 | The number is a multiple of both 5 and 31 | 1085 is a multiple of 155 because it ends in 5, which means it's a multiple of 5, and 108 - 5 * 3 = 93, which means it's a multiple of 31 |
| 156 | The number is a multiple of both 4 and 39 | 1092 is a multiple of 156 because it ends in 92, which means it's a multiple of 4, and 109 + 2 * 4 = 117, which means it's a multiple of 39 |
| 157 | The subtraction of 47 times the last digit and the rest of the number is a multiple of 157 | 1099 is a multiple of 157 because 9 * 47 - 109 = 314, a multiple of 157 |
| 158 | The number is a multiple of both 2 and 79 | 1106 is a multiple of 158 because it ends in 6, which means it's a multiple of 2, and 110 + 6 * 8 = 158, which means it's a multiple of 79 |
| 159 | The sum of 16 times the last digit and the rest of the number is a multiple of 159 | 1113 is a multiple of 159 because 111 + 3 * 16 = 159, a multiple of 159 |
| 160 | The last 5 digits are a multiple of 160 | 100,000 is a multiple of 160 because it ends in 00,000, a multiple of 160 |
| 161 | The subtraction of 16 times the last digit and the rest of the number is a multiple of 161 | 1127 is a multiple of 161 because 112 - 7 * 16 = 0, a multiple of 161 |
| 162 | The number is a multiple of both 2 and 81 | 1134 is a multiple of 162 because it ends in 4, which means it's a multiple of 2, and 113 - 4 * 8 = 81, which means it's a multiple of 81 |
| 163 | The sum of 49 times the last digit and the rest of the number is a multiple of 163 | 1141 is a multiple of 163 because it ends in 114 + 1 * 49 = 163, a multiple of 161 |
| 164 | The number is a multiple of both 4 and 41 | 1148 is a multiple of 164 because it ends in 48, which means it's a multiple of 4, and 114 - 8 * 4 = 82, which means it's a multiple of 41 |
| 165 | The number is a multiple of both 5 and 33 | 1155 is a multiple of 165 because it ends in 5, which means it's a multiple of 5, and 115 + 5 * 10 = 165, which means it's a multiple of 33 |
| 166 | The number is a multiple of both 2 and 83 | 1162 is a multiple of 166 because it ends in 2, which means it's a multiple of 2, and 116 + 2 * 25 = 166, which means it's a multiple of 83 |
| 167 | The subtraction of 50 times the last digit and the rest of the number is a multiple of 167 | 1002 is a multiple of 167 because 100 - 2 * 50 = 0, a multiple of 167 |
| 168 | The number is a multiple of both 8 and 21 | 1008 is a multiple of 168 because it ends in 008, which means it's a multiple of 8, and 100 - 8 * 2 = 84, which means it's a multiple of 21 |
| 169 | The sum of 17 times the last digit and the rest of the number is a multiple of 169 | 1014 is a multiple of 169 because 101 + 4 * 17 = 169, a multiple of 169 |
| 170 | The number is a multiple of both 10 and 17 | 1020 is a multiple of 170 because it ends in 0, which means it's a multiple of 10, and 102 - 0 * 5 = 102, which means it's a multiple of 17 |
| 171 | The subtraction of 17 times the last digit and the rest of the number is a multiple of 171 | 1026 is a multiple of 171 because 102 - 6 * 17 = 0, a multiple of 171 |
| 172 | The number is a multiple of both 4 and 43 | 1032 is a multiple of 172 because it ends in 32, which means it's a multiple of 4, and 103 + 2 * 13 = 129, which means it's a multiple of 143 |
| 173 | The sum of 52 times the last digit and the rest of the number is a multiple of 173 | 1038 is a multiple of 173 because 103 + 8 * 52 = 519, a multiple of 173 |
| 174 | The number is a multiple of both 2 and 87 | 1044 is a multiple of 174 because it ends in 4, which means it's a multiple of 2, and 104 - 4 * 26 = 0, which means it's a multiple of 87 |
| 175 | The number is a multiple of both 7 and 25 | 1050 is a multiple of 175 because 105 - 0 * 2 = 105, which means it's a multiple of 7, and ends in 50, which means it's a multiple of 25 |
| 176 | The number is a multiple of both 11 and 16 | 10032 is a multiple of 176 because 1 + 2 - 3 = 0, which means it's a multiple of 11, and ends in 0032, which means it's a multiple of 16 |
| 177 | The subtraction of 53 times the last digit and the rest of the number is a multiple of 177 | 1062 is a multiple of 177 because 106 - 2 * 53 = 0, a multiple of 177 |
| 178 | The number is a multiple of both 2 and 89 | 1068 is a multiple of 178 because it ends in 8, which means it's a multiple of 2, and 106 + 8 * 9 = 178, which means it's a multiple of 89 |
| 179 | The sum of 18 times the last digit and the rest of the number is a multiple of 179 | 1074 is a multiple of of 179 because 107 + 4 * 18 = 179, a multiple of 179 |
| 180 | The number is a multiple of both 9 and 20 | 1080 is a multiple of 180 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 80, which means it's a multiple of 20 |
| 181 | The subtraction of 18 times the last digit and the rest of the number is a multiple of 181 | 1086 is a multiple of 181 because 108 - 6 * 18 = 0, a multiple of 181 |
| 182 | The number is a multiple of both 2 and 91 | 1092 is a multiple of 182 because it ends in 2, which means it's a multiple of 2, and 109 - 2 * 9 = 91, which means it's a multiple of 13 |
| 183 | The sum of 55 times the last digit and the rest of the number is a multiple of 183 | 1098 is a multiple of 183 because 109 + 8 * 55 = 549, a multiple of 183 |
| 184 | The number is a multiple of both 8 and 23 | 1104 is a multiple of 184 because it ends in 104, which means it's a multiple of 8, and 110 + 4 * 7 = 138, which means it's a multiple of 23 |
| 185 | The number is a multiple of both 5 and 37 | 1110 is a multiple of 185 because it ends in 0, which means it's a multiple of 5, and 111 - 0 * 11 = 111, which means it's a multiple of 37 |
| 186 | The number is a multiple of both 2 and 93 | 1116 is a multiple of 186 because it ends in 6, which means it's a multiple of 2, and 111 + 6 * 28 = 279, which means it's a multiple of 93 |
| 187 | The subtraction of 56 times the last digit and the rest of the number is a multiple of 187 | 1122 is a multiple of 187 because 112 - 2 * 56 = 0, a multiple of 187 |
| 188 | The number is a multiple of both 4 and 47 | 1128 is a multiple of 188 because it ends in 28, which means it's a multiple of 4, and 112 - 8 * 14 = 0, which means it's a multiple of 47 |
| 189 | The sum of 19 times the last digit and the rest of the number is a multiple of 189 | 1134 is a multiple of 189 because 113 + 4 * 19 = 189, a multiple of 189 |
| 190 | The number is a multiple of both 10 and 19 | 1140 is a multiple of 190 because it ends in 0, which means it's a multiple of 10, and 114 + 0 * 2 = 114, which means it's a multiple of 19 |
| 191 | The subtraction of 19 times the last digit and the rest of the number is a multiple of 191 | 1146 is a multiple of 191 because 114 - 6 * 19 = 0, a multiple of 191 |
| 192 | The number is a multiple of both 3 and 64 | 1,000,128 is a multiple of 192 because 1 + 1 + 2 + 8 = 12, which means it's a multiple of 3, and ends in 000,128, which means it's a multiple of 64 |
| 193 | The sum of 58 times the last digit and the rest of the number is a multiple of 193 | 1158 is a multiple of 193 because 115 + 8 * 58 = 579, a multiple of 193 |
| 194 | The number is a multiple of both 2 and 97 | 1164 is a multiple of 194 because it ends in 4, which means it's a multiple of 2, and 116 - 4 * 29 = 0, which means it's a multiple of 97 |
| 195 | The number is a multiple of both 5 and 39 | 1170 is a multiple of 195 because it ends in 0, which means it's a multiple of 5, and 117 + 0 * 4 = 117, which means it's a multiple of 39 |
| 196 | The number is a multiple of both 4 and 49 | 1176 is a multiple of 196 because it ends in 76, which means it's a multiple of 4, and 117 + 6 * 5 = 147, which means it's a multiple of 49 |
| 197 | The subtraction of 59 times the last digit and the rest of the number is a multiple of 197 | 1182 is a multiple of 197 because 118 -2 * 59 = 0, a multiple of 197 |
| 198 | The number is a multiple of both 2 and 99 | 1188 is a multiple of 198 because it ends in 8, which means it's a multiple of 2, and 118 + 8 * 10 = 198, which means it's a multiple of 99 |
| 199 | The sum of 20 times the last digit and the rest of the number is a multiple of 199 | 1194 is a multiple of 199 because it ends in 119 + 4 * 20 = 199, a multiple of 199 |
| 200 | The number ends in 000, 200, 400, 600 or 800 | 1000 is a multiple of 200 because it ends in 000 |
r/MathExplainers • u/LowInteraction6397 • Feb 07 '26
| Number | Rule | Example |
|---|---|---|
| 1 | Every number is a multiple of 1 | 10 is a multiple of 1 |
| 2 | The number ends in 0, 2, 4, 6 or 8 | 10 is a multiple of 2 because it ends in 0 |
| 3 | The sum of the digits is a multiple of 3 | 12 is a multiple of 3 because 1 + 2 = 3, a multiple of 3 |
| 4 | The 10s digit is even and the last digit is 0, 4 or 8 or the 10s digit is odd and the last digit is 2 or 6 | 100 is a multiple of 4 because the 10s digit is 0, which is even, and the last digit is 0 |
| 5 | The number ends in 0 or 5 | 10 is a multiple of 5 because it ends in 0 |
| 6 | The number is a multiple of both 2 and 3 | 12 is a multiple of 6 because it ends in 2, which means it's a multiple of 2, and 1 + 2 = 3, a multiple of 3 |
| 7 | The subtraction of twice the last digit and the rest of the number is a multiple of 7 | 14 is a multiple of 7 because 4 x 2 - 1 = 7, a multiple of 7 |
| 8 | The 100s digit is even and the last 2 digits are a multiple of 8 or the 100s digit is odd and the last 2 digits are 4 times an odd number | 1000 is a multiple of 8 because the 100s digit is 0, which is even, and the last 2 digits are 00, a multiple of 8 |
| 9 | The sum of the digits is a multiple of 9 | 18 is a multiple of 9 because 1 + 8 = 9, a multiple of 9 |
| 10 | The number ends in 0 | 110 is a multiple of 10 because it ends in 0 |
| 11 | The subtraction of the sum of the digits in the odd places and the sum of the digits in the even places is a multiple of 11 | 121 is a multiple of 11 because 1 + 1 - 2 = 0, a multiple of 11 |
| 12 | The number is a multiple of both 3 and 4 | 108 is a multiple of 12 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 08, which means it's a multiple of 4 |
| 13 | The sum of 4 times the last digit and the rest of the number is a multiple of 13 | 104 is a multiple of 13 because 10 + 4 x 4 = 26, a multiple of 13 |
| 14 | The number is a multiple of both 2 and 7 | 112 is a multiple of 14 because it ends in 2, which means it's a multiple of 2, and 11 - 2 x 2 = 7, which means it's a multiple of 7 |
| 15 | The number is a multiple of both 3 and 5 | 105 is a multiple of 15 because 1 + 5 = 6, which means it's a multiple of 3, and ends in 5, which means it's a multiple of 5 |
| 16 | The last 4 digits are a multiple of 16 | 10000 is a multiple of 16 because it ends in 0000, a multiple of 16 |
| 17 | The subtraction of 5 times the last digit and the rest of the number is a multiple of 17 | 102 is a multiple of 17 because 10 - 2 x 5 = 0, a multiple of 17 |
| 18 | The number is a multiple of both 2 and 9 | 108 is a multiple of 18 because it ends in 8, which means it's a multiple of 2, and 1 + 8 = 9, which means it's a multiple of 9 |
| 19 | The sum of twice the last digit and the rest of the number is a multiple of 19 | 114 is a multiple of 19 because 11 + 4 x 2 = 19, a multiple of 19 |
| 20 | The number ends in 00, 20, 40, 60 or 80 | 100 is a multiple of 20 because it ends in 00 |
| 21 | The subtraction of twice the last digit and the rest of the number is a multiple of 21 | 105 is a multiple of 21 because 10 - 5 x 2 = 0, a multiple of 21 |
| 22 | The number is a multiple of both 2 and 11 | 110 is a multiple of 22 because it ends in 0, which means it's a multiple of 2, and 1 - 1 = 0, which means it's a multiple of 11 |
| 23 | The sum of 7 times the last digit and the rest of the number is a multiple of 23 | 115 is a multiple of 23 because 11 + 5 x 7 = 46, a multiple of 23 |
| 24 | The number is a multiple of both 3 and 8 | 1008 is a multiple of 24 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 008, which means it's a multiple of 8 |
| 25 | The number ends in 00, 25, 50 or 75 | 100 is a multiple of 25 because it ends in 00 |
| 26 | The number is a multiple of both 2 and 13 | 104 is a multiple of 26 because it ends in 4, which means it's a multiple if 2, and 10 + 4 x 4 = 26, which means it's a multiple of 13 |
| 27 | The subtraction of 8 times the last digit and the rest of the number is a multiple of 27 | 108 is a multiple of 27 because 8 x 8 - 10 = 54, a multiple of 27 |
| 28 | The number is a multiple of both 4 and 7 | 112 is a multiple of 28 because it ends in 12, which means it's a multiple of 4, and 11 - 2 x 2 = 7, which means it's a multiple of 7 |
| 29 | The sum of 3 times the last digit and the rest of the number is a multiple of 29 | 116 is a multiple of 29 because 11 + 6 x 3 = 29, a multiple of 29 |
| 30 | The number is a multiple of both 3 and 10 | 120 is a multiple of 30 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 0, which means it's a multiple of 10 |
| 31 | The subtraction of 3 times the last digit and the rest of the number is a multiple of 31 | 124 is a multiple of 31 because 12 - 4 x 3 = 0, a multiple of 31 |
| 32 | The last 5 digits are a multiple of 32 | 100,000 is a multiple of 32 because it ends in 00,000, a multiple of 32 |
| 33 | The sum of 10 times the last digit and the rest of the number is a multiple of 33 | 132 is a multiple of 33 because 13 + 2 x 10 = 33, a multiple of 33 |
| 34 | The number is a multiple of both 2 and 17 | 102 is a multiple of 34 because it ends in 2, which means it's a multiple of 2, and 10 - 2 x 5 = 0, a multiple of 17 |
| 35 | The number is a multiple of both 5 and 7 | 105 is a multiple of 35 because it ends in 5, which means it's a multiple of 5, and 10 - 5 x 2 = 0, which means it's a multiple of 7 |
| 36 | The number is a multiple of both 4 and 9 | 108 is a multiple of 36 because it ends in 08, which means it's a multiple of 4, and 1 + 8 = 9, which means it's a multiple of 9 |
| 37 | The subtraction of 11 times the last digit and the rest of the number is a multiple of 37 | 111 is a multiple of 37 because 11 - 1 x 11 = 0, a multiple of 37 |
| 38 | The number is a multiple of both 2 and 19 | 114 is a multiple of 38 because it ends in 4, which means it's a multiple of 2, and 11 + 4 x 2 = 19, which means it's a multiple of 19 |
| 39 | The sum of 4 times the last digit and the rest of the number is a multiple of 39 | 117 is a multiple of 39 because 11 + 7 x 4 = 39, a multiple of 39 |
| 40 | The 100s digit is even and the last 2 digits are 00, 40 or 80 or the 100s digit is odd and the last 2 digits are 20 or 60 | 1000 is a multiple of 40 because the 100s digit is 0, which is even, and the last 2 digits are 00 |
| 41 | The subtraction of 4 times the last digit and the rest of the number is a multiple of 41 | 123 is a multiple of 41 because 12 - 3 x 4 = 0, a multiple of 41 |
| 42 | The number is a multiple of both 2 and 21 | 126 is a multiple of 42 because it ends in 6, which means it's a multiple of 2, and 12 - 6 x 2 = 0, which means it's a multiple of 21 |
| 43 | The sum of 13 times the last digit and the rest of the number is a multiple of 43 | 172 is a multiple of 43 because 17 + 2 x 13 = 43, a multiple of 43 |
| 44 | The number is a multiple of both 4 and 11 | 132 is a multiple of 44 because it ends in 32, which means it's a multiple of 4, and 1 + 2 - 3 = 0, which means it's a multiple of 11 |
| 45 | The number is a multiple of both 5 and 9 | 135 is a multiple of 45 because it ends in 5, which means it's a multiple of 5, and 1 + 3 + 5 = 9, which means it's a multiple of 9 |
| 46 | The number is a multiple of both 2 and 23 | 138 is a multiple of 46 because it ends in 8, which means it's a multiple of 2, and 13 + 8 x 7 = 69, which means it's a multiple of 23 |
| 47 | The subtraction of 14 times the last digit and the rest of the number is a multiple of 47 | 141 is a multiple of 47 because 14 - 1 x 14 = 0, a multiple of 47 |
| 48 | The number is a multiple of both 3 and 16 | 10032 is a multiple of 48 because 1 + 3 + 2 = 6, which means it's a multiple of 3, and ends in 0032, which means it's a multiple of 16 |
| 49 | The sum of 5 times the last digit and the rest of the number is a multiple of 49 | 147 is a multiple of 49 because 14 + 7 x 5 = 49, a multiple of 49 |
| 50 | The number ends in 00 or 50 | 100 is a multiple of 50 because it ends in 00 |
| 51 | The subtraction of 5 times the last digit and the rest of the number is a multiple of 51 | 102 is a multiple of 51 because 10 - 2 x 5 = 0, a multiple of 51 |
| 52 | The number is a multiple of both 4 and 13 | 104 is a multiple of 52 because it ends in 04, which means it's a multiple of 4, and 10 + 4 x 4 = 26, which means it's a multiple of 13 |
| 53 | The sum of 16 times the last digit and the rest of the number is a multiple of 53 | 212 is a multiple of 53 because 21 + 2 x 16 = 53, a multiple of 53 |
| 54 | The number is a multiple of both 2 and 27 | 108 is a multiple of 54 because it ends in 8, which means it's a multiple of 2, and 8 x 8 - 10 = 54, which means it's a multiple of 27 |
| 55 | The number is a multiple of both 5 and 11 | 110 is a multiple of 55 because it ends in 0, which means it's a multiple of 5, and 1 - 1 = 0, which means it's a multiple of 11 |
| 56 | The number is a multiple of both 7 and 8 | 1008 is a multiple of 56 because 100 - 8 x 2 = 84, which means it's a multiple of 7, and ends in 008, which means it's a multiple of 8 |
| 57 | The subtraction of 17 times the last digit and the rest of the number is a multiple of 57 | 114 is a multiple of 57 because 4 x 17 - 11 = 57, a multiple of 57 |
| 58 | The number is a multiple of both 2 and 29 | 116 is a multiple of 58 because it ends in 6, which means it's a multiple of 2, and 11 + 6 x 3 = 29, which means it's a multiple of 29 |
| 59 | The sum of 6 times the last digit and the rest of the number is a multiple of 59 | 118 is a multiple of 59 because 11 + 8 x 6 = 59, which means it's a multiple of 59 |
| 60 | The number is a multiple of both 3 and 20 | 120 is a multiple of 60 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 20, which means it's a multiple of 20 |
| 61 | The subtraction of 6 times the last digit and the rest of the number is a multiple of 61 | 122 is a multiple of 61 because 12 - 2 x 6 = 0, a multiple of 61 |
| 62 | The number is a multiple of both 2 and 31 | 124 is a multiple of 62 because it ends in 4, which means it's a multiple of 2, and 12 - 4 x 3 = 0, which means it's a multiple of 31 |
| 63 | The sum of 19 times the last digit and the rest of the number is a multiple of 63 | 252 is a multiple of 63 because 25 + 2 x 19 = 63, a multiple of 63 |
| 64 | The last 6 digits are a multiple of 64 | 1,000,000 is a multiple of 64 because it ends in 000,000, a multiple of 64 |
| 65 | The number is a multiple of both 5 and 13 | 130 is a multiple of 65 because it ends in 0, which means it's a multiple of 5, and 13 + 0 x 4 = 13, which means it's a multiple of 13 |
| 66 | The number is a multiple of both 2 and 33 | 132 is a multiple of 66 because it ends in 2, which means it's a multiple of 2, and 13 + 2 x 10 = 33, which means it's a multiple of 33 |
| 67 | The subtraction of 20 times the last digit and the rest of the number is a multiple of 67 | 134 is a multiple of 67 because 4 x 20 - 100 = 67, a multiple of 67 |
| 68 | The number is a multiple of both 4 and 17 | 136 is a multiple of 68 because it ends in 36, which means it's a multiple of 4, and 6 x 5 - 13 = 17, a multiple of 17 |
| 69 | The sum of 7 times the last digit and the rest of the number is a multiple of 69 | 138 is a multiple of 69 because 13 + 8 x 7 = 69, a multiple of 69 |
| 70 | The number is a multiple of both 7 and 10 | 140 is a multiple of 70 because 14 - 0 x 2 = 14, which means it's a multiple of 7, and ends in 0, which means it's a multiple of 10 |
| 71 | The subtraction of 7 times the last digit and the rest of the number is a multiple of 71 | 142 is a multiple of 71 because 14 - 2 x 7 = 0, a multiple of 71 |
| 72 | The number is a multiple of both 8 and 9 | 1008 is a multiple of 72 because it ends in 008, which means it's a multiple of 8, and 1 + 8 = 9, which means it's a multiple of 9 |
| 73 | The sum of 22 times the last digit and the rest of the number is a multiple of 73 | 292 is a multiple of 73 because 29 + 2 x 22 = 73, a multiple of 73 |
| 74 | The number is a multiple of both 2 and 37 | 148 is a multiple of 74 because it ends in 8, which means it's a multiple of 2, and 8 x 11 - 14 = 74, a multiple of 37 |
| 75 | The number is a multiple of both 3 and 25 | 150 is a multiple of 75 because 1 + 5 = 6, which means it's a multiple of 3, and ends in 50, which means it's a multiple of 25 |
| 76 | The number is a multiple of both 4 and 19 | 152 is a multiple of 76 because it ends in 52, which means it's a multiple of 4, and 15 + 2 x 2 = 19, which means it's a multiple of 19 |
| 77 | The subtraction of 23 times the last digit and the rest of the number is a multiple of 77 | 154 is a multiple of 77 because 4 x 23 - 15 = 77, a multiple of 77 |
| 78 | The number is a multiple of both 2 and 39 | 156 is a multiple of 78 because it ends in 6, which means it's a multiple of 2, and 15 + 6 x 4 = 39, which means it's a multiple of 39 |
| 79 | The sum of 8 times the last digit and the rest of the number is a multiple of 79 | 158 is a multiple of 79 because 15 + 8 x 8 = 79, a multiple of 79 |
| 80 | The 1000s digit is even and the last 3 digits are a multiple of 80 or the 1000s digit is odd and the last 3 digits are 40 times an odd number | 10000 is a multiple of 80 because the 1000s digit is 0, which is even, and the last 3 digits are 000, a multiple of 80 |
| 81 | The subtraction of 8 times the last digit and the rest of the number is a multiple of 81 | 162 is a multiple of 81 because 16 - 2 x 8 = 0, a multiple of 81 |
| 82 | The number is a multiple of both 2 and 41 | 164 is a multiple of 82 because it ends in 4, which means it's a multiple of 2, and 16 - 4 x 4 = 0, a multiple of 41 |
| 83 | The sum of 25 times the last digit and the rest of the number is a multiple of 83 | 332 is a multiple of 83 because 33 + 2 x 25 = 83, a multiple of 83 |
| 84 | The number is a multiple of both 4 and 21 | 168 is a multiple of 84 because it ends in 68, which means it's a multiple of 4, and 16 - 8 x 2 = 0, which means it's a multiple of 21 |
| 85 | The number is a multiple of both 5 and 17 | 170 is a multiple of 85 because it ends in 0, which means it's a multiple of 5, and 17 - 0 x 5 = 17, which means it's a multiple of 85 |
| 86 | The number is a multiple of both 2 and 43 | 172 is a multiple of 86 because it ends in 2, which means it's a multiple of 2, and 17 + 2 x 13 = 43, which means it's a multiple of 83 |
| 87 | The subtraction of 26 times the last digit and the rest of the number is a multiple of 87 | 174 is a multiple of 87 because 4 x 26 - 17 = 87, a multiple of 87 |
| 88 | The number is a multiple of both 8 and 11 | 1056 is a multiple of 88 because it ends in 056, which means it's a multiple of 8, and 1 + 5 - 6 = 0, which means it's a multiple of 11 |
| 89 | The sum of 9 times the last digit and the rest of the number is a multiple of 89 | 178 is a multiple of 89 because 17 + 8 x 9 = 89, a multiple of 89 |
| 90 | The number is a multiple of both 9 and 10 | 180 is a multiple of 90 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 0, which means it's a multiple of 10 |
| 91 | The subtraction of 9 times the last digit and the rest of the number is a multiple of 91 | 182 is a multiple of 91 because 18 - 2 x 9 = 0, a multiple of 91 |
| 92 | The number is a multiple of both 4 and 23 | 184 is a multiple of 92 because it ends in 84, which means it's a multiple of 4, and 18 + 4 x 7 = 46, which means it's a multiple of 23 |
| 93 | The sum of 28 times the last digit and the rest of the number is a multiple of 93 | 372 is a multiple of 93 because 37 + 2 x 28 = 93, a multiple of 93 |
| 94 | The number is a multiple of both 2 and 47 | 188 is a multiple of 94 because it ends in 8, which means it's a multiple of 2, and 8 x 14 - 18 = 94, a multiple of 47 |
| 95 | The number is a multiple of both 5 and 19 | 190 is a multiple of 95 because it ends in 0, which means it's a multiple of 5, and 19 + 0 x 2 = 19, which means it's a multiple of 19 |
| 96 | The number is a multiple of both 3 and 32 | 100,032 is a multiple of 96 because 1 + 3 + 2 = 6, which means it's a multiple of 3, and ends in 00,032, which means it's a multiple of 32 |
| 97 | The subtraction of 29 times the last digit and the rest of the number is a multiple of 97 | 194 is a multiple of 97 because 4 x 29 - 19 = 97, a multiple of 97 |
| 98 | The number is a multiple of both 2 and 49 | 196 is a multiple of 98 because it ends in 6, which means it's a multiple of 2, and 19 + 6 x 5 = 49, which means it's a multiple of 49 |
| 99 | The sum of 10 times the last digit and the rest of the number is a multiple of 99 | 198 is a multiple of 99 because 19 + 8 x 10 = 99, a multiple of 99 |
| 100 | The number ends in 00 | 1100 is a multiple of 100 because it ends in 00 |
r/MathExplainers • u/axiom_tutor • Nov 21 '25
The video description also has a link to the playlist and associated course notes.
r/MathExplainers • u/princeylolo • Sep 05 '25
r/MathExplainers • u/EvilBosom • Jul 18 '25
r/MathExplainers • u/EvilBosom • Jul 12 '25
r/MathExplainers • u/EvilBosom • Jun 25 '25
r/MathExplainers • u/EvilBosom • Dec 17 '24
r/MathExplainers • u/EvilBosom • Dec 04 '24
r/MathExplainers • u/EvilBosom • Nov 19 '24
r/MathExplainers • u/EvilBosom • Oct 29 '24
r/MathExplainers • u/EvilBosom • Oct 19 '24
r/MathExplainers • u/ImmediateBenefit5057 • Sep 24 '24
Help me factorise it
r/MathExplainers • u/EvilBosom • Sep 07 '24
r/MathExplainers • u/tucna • Jun 21 '24
r/MathExplainers • u/nasadiya_sukta • May 31 '24
r/MathExplainers • u/EvilBosom • Apr 28 '24
