Please consider helping us with an online survey which is part of an academic research project. The survey should not take longer than 10 minutes.

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? (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 ...)

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) |

Back To All Divisibility Rules

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 |

Back To All Divisibility Rules

Rule: If the last two digits are a multiple of 4 | ||

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 |

Back To All Divisibility Rules

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) |

Back To All Divisibility Rules

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 ) 5 + 9 + 1 + 2 = 17 (17 is |

508 | No | The last digit is a 8 (it is a multiple of 2 ) 5 + 0 + 8 = 13 (13 is |

Back To All Divisibility Rules

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 |

Back To All Divisibility Rules

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) |