Divisibility rules help us work out whether a number is exactly divisible by other numbers (i.e. there is no remainder).
The rules are shortcuts for finding out whether numbers are exactly divisible without doing division calculations. Some of these rules along with examples are illustrated below:
Number | Divisible? | Why? |
456 | Yes | The last digit is 6 |
68 | Yes | The last digit is 8 |
25 | No | The last digit is 5 (not a 2,4,6,or 8) |
207 | No | The last digit is 7 (not a 2,4,6,or 8) |
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Number | Divisible? | Why? |
405 | Yes | 4 + 0 + 5 = 9 (9 is a multiple of 3) |
381 | Yes | 3 + 8 + 1 = 12 (12 is a multiple of 3) |
928 | No | 9 + 2 + 8 = 19 (19 is not a multiple of 3) |
4,616 | No | 4 + 6 + 1 + 6 = 17 (17 is not a multiple of 3) |
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 |
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Number | Divisible? | Why? |
348 | Yes | 48 is a multiple of 4 |
27,616 | Yes | 16 is a multiple of 4 |
8,514 | No | 14 is not a multiple of 4 |
722 | No | 22 is not a multiple of 4 |
1,200 | Yes | The last two digits are 00 200 is a multiple of 4 |
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 |
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Number | Divisible? | Why? |
3,425 | Yes | The last digit is 5 |
750 | Yes | The last digit is 0 |
8,551 | No | The last digit is 1 (not a 0 or a 5) |
394 | No | The last digit is 4 (not a 0 or a 5) |
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Number | Divisible? | Why? |
5,106 | Yes |
The last digit is a 2 (it is a multiple of 2 ) and... 5 + 1 + 0 + 6 = 12 (12 is a multiple of 3) |
636 | Yes |
The last digit is a 6 (it is a multiple of 2 ) and... 6 + 3 + 6 = 15 (15 is a multiple of 3) |
5,912 | No |
The last digit is a 2 (it is a multiple of 2 ) but... 5 + 9 + 1 + 2 = 17 (17 is not a multiple of 3) |
508 | No |
The last digit is a 8 (it is a multiple of 2 ) but... 5 + 0 + 8 = 13 (13 is not a multiple of 3) |
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Number | Divisible? | Why? |
7,686 | Yes | 7 + 6 + 8 + 6 = 27 (27 is a multiple of 9) |
252 | Yes | 2 + 5 + 2 = 9 (9 is a multiple of 9) |
883 | No | 8 + 8 + 3 = 19 (19 is not a multiple of 9) |
5,105 | No | 5 + 1 + 0 + 5 = 11 (11 is not a multiple of 9) |
9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 |
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Number | Divisible? | Why? |
880 | Yes | The last digit is 0 |
9,560 | Yes | The last digit is 0 |
312 | No | The last digit is 2 (not a 0) |
7,897 | No | The last digit is 7 (not a 0) |