| Number | Divisible by | Rule | Example |
| ABCDEF | 2 | If 'F' is even | 112 (Last digit is 2, which is even) |
| ABCDEF | 3 | If 'A+B+C+D+E+F' is divisible by 3 | 396 (3+9+6 = 18, which is divisible by 3) |
| ABCDEF | 4 | If 'EF' is divisible by 4 | 112 (Last 2 digit is 12, which is divisible by 4) |
| ABCDEF | 5 | If 'F' is 0 or 5 | 105 (Last digit is 5) |
| ABCDEF | 6 | If 'ABCDEF' is divisible by 2 and 3 |
| ABCDEF | 7 | If 'ABCDE - 2×F' is divisible by 7 (Apply this rule to the answer again if necessary) | Check 9464 is divisible by 7 or not 9464 `=>` 946 - 4 × 2 = 946 - 8 = 938 938 `=>` 93 - 8 × 2 = 93 - 16 = 77 Here 77 is divisible by 7 So 9464 is divisible by 7 |
| ABCDEF | 8 | If 'DEF' is divisible by 8 | 5816 (Last 3 digit is 816, which is divisible by 8) |
| ABCDEF | 9 | If 'A+B+C+D+E+F' is divisible by 9 | 396 (3+9+6 = 18, which is divisible by 9) |
| ABCDEF | 10 | If 'F' is 0 | 150 (Last digit is 0) |
| ABCDEF | 11 (method-1) | (Sum of digits in odd positions) - (Sum of digits in even positions) is 0 or divisible by 11. | 2563 = [(5+3) - (2+6) = 0, which is 0] 7392 = [(3+2) - (7+9) = -11, which is divisible by 11] |
| ABCDEF | 11 (method-2) | If 'ABCDE - F' is divisible by 11 (Apply this rule to the answer again if necessary) | Check 2563 is divisible by 11 or not 2563 `=>` 256 - 3 = 253 253 `=>` 25 - 3 = 22 Here 22 is divisible by 11 So 2563 is divisible by 11 |
| ABCDEF | 12 | If 'ABCDEF' is divisible by 3 and 4 |
| ABCDEF | 13 | If 'ABCDE + 4×F' is divisible by 13 (Apply this rule to the answer again if necessary). | Check 13273 is divisible by 13 or not 13273 `=>` 1327 + 3 × 4 = 1327 + 12 = 1339 1339 `=>` 133 + 9 × 4 = 133 + 36 = 169 169 `=>` 16 + 9 × 4 = 16 + 36 = 52 Here 52 is divisible by 13 So 13273 is divisible by 13 |
| ABCDEF | 14 | If 'ABCDEF' is divisible by 2 and 7 |
| ABCDEF | 15 | If 'ABCDEF' is divisible by 3 and 5 |
| ABCDEF | 16 | If 'CDEF' is divisible by 16 | 10256 (Last 4 digit is 0256, which is divisible by 16) - Yes 10255 (Last 4 digit is 0255, which is not divisible by 16) - No |
| ABCDEF | 17 | If 'ABCDE - 5×F' is divisible by 17 (Apply this rule to the answer again if necessary). | Check 17544 is divisible by 17 or not 17544 `=>` 1754 - 4 × 5 = 1754 - 20 = 1734 1734 `=>` 173 - 4 × 5 = 173 - 20 = 153 153 `=>` 15 - 3 × 5 = 15 - 15 = 0 Here 0 is divisible by 17 So 17544 is divisible by 17 |
| ABCDEF | 18 | If 'ABCDEF' is divisible by 2 and 9 |
| ABCDEF | 19 | If 'ABCDE + 2×F' is divisible by 19 (Apply this rule to the answer again if necessary). | Check 19456 is divisible by 19 or not 19456 `=>` 1945 + 6 × 2 = 1945 + 12 = 1957 1957 `=>` 195 + 7 × 2 = 195 + 14 = 209 209 `=>` 20 + 9 × 2 = 20 + 18 = 38 Here 38 is divisible by 19 So 19456 is divisible by 19 |
| ABCDEF | 20 | If 'ABCDEF' is divisible by 4 and 5 |
| ABCDEF | 21 | If 'ABCDEF' is divisible by 3 and 7 |
| ABCDEF | 22 | If 'ABCDEF' is divisible by 2 and 11 |
| ABCDEF | 23 | If 'ABCDE + 7×F' is divisible by 23 (Apply this rule to the answer again if necessary). | Check 29946 is divisible by 23 or not 29946 `=>` 2994 + 6 × 7 = 2994 + 42 = 3036 3036 `=>` 303 + 6 × 7 = 303 + 42 = 345 345 `=>` 34 + 5 × 7 = 34 + 35 = 69 Here 69 is divisible by 23 So 29946 is divisible by 23 |
| ABCDEF | 24 | If 'ABCDEF' is divisible by 3 and 8 |
| ABCDEF | 25 | If 'EF' is divisible by 25 |
| ABCDEF | 26 | If 'ABCDEF' is divisible by 2 and 13 |
| ABCDEF | 27 | If 'ABCDE - 8×F' is divisible by 27 (Apply this rule to the answer again if necessary). |
| ABCDEF | 28 | If 'ABCDEF' is divisible by 4 and 7 |
| ABCDEF | 29 | If 'ABCDE + 3×F' is divisible by 29 (Apply this rule to the answer again if necessary). | Check 37758 is divisible by 29 or not 37758 `=>` 3775 + 8 × 3 = 3775 + 24 = 3799 3799 `=>` 379 + 9 × 3 = 379 + 27 = 406 406 `=>` 40 + 6 × 3 = 40 + 18 = 58 Here 58 is divisible by 29 So 37758 is divisible by 29 |
| ABCDEF | 30 | If 'ABCDEF' is divisible by 2,3 and 5 |
| ABCDEF | 31 | If 'ABCDE - 3×F' is divisible by 31 (Apply this rule to the answer again if necessary). | Check 2263 is divisible by 31 or not `2263=>226 - 3 xx 3 = 226 -9 = 217` `217=>21 - 7 xx 3 = 21 -21 = 0` Here 0 is divisible by 31. So 2263 is divisible by 31. |
| ABCDEF | 32 | If 'BCDEF' is divisible by 32 |
| ABCDEF | 33 | If 'ABCDEF' is divisible by 3 and 11 |
| ABCDEF | 34 | If 'ABCDEF' is divisible by 2 and 17 |
| ABCDEF | 35 | If 'ABCDEF' is divisible by 5 and 7 |
| ABCDEF | 36 | If 'ABCDEF' is divisible by 4 and 9 |
| ABCDEF | 37 | If 'ABCDE - 11×F' is divisible by 37 (Apply this rule to the answer again if necessary). | Check 2701 is divisible by 37 or not `2701=>270 - 1 xx 11 = 270 -11 = 259` `259=>25 - 9 xx 11 = 25 -99 = -74` Here -74 is divisible by 37.So 2701 is divisible by 37. |
| ABCDEF | 38 | If 'ABCDEF' is divisible by 2 and 19 |
| ABCDEF | 39 | If 'ABCDEF' is divisible by 3 and 13 |
| ABCDEF | 39 | If 'ABCDE + 4×F' is divisible by 39 (Apply this rule to the answer again if necessary). | Check 5226 is divisible by 39 or not `522color{red}{6}=>522 + color{red}{6} xx 4 = 522 +24 = 546` `54color{red}{6}=>54 + color{red}{6} xx 4 = 54 +24 = 78` Here 78 is divisible by 39. `:.` 5226 is divisible by 39. |
| ABCDEF | 40 | If 'ABCDEF' is divisible by 5 and 8 |
| ABCDEF | 41 | If 'ABCDE - 4×F' is divisible by 41 (Apply this rule to the answer again if necessary). | Check 2993 is divisible by 41 or not `2993=>299 - 3 xx 4 = 299 -12 = 287` `287=>28 - 7 xx 4 = 28 -28 = 0` Here 0 is divisible by 41.So 2993 is divisible by 41. |
| ABCDEF | 42 | If 'ABCDEF' is divisible by 2, 3 and 7 |
| ABCDEF | 43 | If 'ABCDE + 13×F' is divisible by 43 (Apply this rule to the answer again if necessary). | Check 3139 is divisible by 43 or not `3139=>313 + 9 xx 13 = 313 +117 = 430` `430=>43 + 0 xx 13 = 43 = 43` Here 43 is divisible by 43. So 3139 is divisible by 43. |
| ABCDEF | 44 | If 'ABCDEF' is divisible by 4 and 11 |
| ABCDEF | 45 | If 'ABCDEF' is divisible by 5 and 9 |
| ABCDEF | 46 | If 'ABCDEF' is divisible by 2 and 23 |
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