Divisibility Rules
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:
Divisible by 2?
| Rule: If it ends with a 0, 2, 4, 6, or 8 | ||
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| 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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Divisible by 3?
| Rule: If the sum of the digits is a multiple of 3 | ||
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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) |
| Helper: The multiples of 3 include... | ||||||||||||||
| 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 |
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Divisible by 4?
| Rule: If the last two digits are a multiple of 4 | ||
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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 |
| Helper: The multiples of 4 include... | ||||||||||||||
| 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 |
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Divisible by 5?
| Rule: If it ends with a 5 or a 0 | ||
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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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Divisible by 6?
| Rule: If it is divisible by 2 and by 3 | ||
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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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Divisible by 9?
| Rule: If the sum of the digits are a multiple of 9 | ||
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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) |
| Helper: The multiples of 9 include... | ||||||||||||||
| 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 |
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Divisible by 10?
| Rule: If the last digit is 0 | ||
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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) |
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