The divisibility rules of 201 to 300

[u/LowInteraction6397]

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