Divisibility rules help us work out whether a number is exactly divisible by other numbers (i.e. there is no remainder).

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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? (Click For Rule ...)
- Divisible by 3? (Click For Rule ...)
- Divisible by 4? (Click For Rule ...)
- Divisible by 5? (Click For Rule ...)
- Divisible by 6? (Click For Rule ...)
- Divisible by 9? (Click For Rule ...)
- Divisible by 10? (Click For Rule ...)

**Divisible by 2?**

Rule: If it ends with a 0, 2, 4, 6, or 8

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

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

(or if the last two digits are 00)

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 |

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

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

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

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

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) |