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:

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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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Rule: If the last two digits are a multiple of 4 (or if the last two digits are 00) |
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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 |

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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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 |

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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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Back To All Divisibility Rules

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