## Factors and Divisibility

When two non-zero integers are multiplied, each integer is a* factor* of the product.

For example, 4 *×* 5 = 20, so 4 and 5 are factors of 20.

The integer *a* is said to be divisible by the integer *b* if *b* is a factor of *a*. This means *a* can be divided by *b* with an integer result (meaning there is no remainder).

For example, 20 is divisible by 4 because 4 is a factor of 20, so 20/4 = 5. On the other hand, 8 is not a factor of 20 because 20/8 = 2.5, and 2.5 is not an integer.

### Rules of Divisibility

#### Number Rule

1 |
All integers are divisible by 1. |

2 |
All integers with a units digit of 0, 2, 4, 6, or 8 are divisible by 2. |

3 |
If the sum of an integer’s digits is divisible by 3, then the integer is divisible by 3. For example, 222 consists of digits that add to 6, so the integer is divisible by 3 (222 / 3 = 74). |

4 |
An integer is divisible by 4 if the number formed by its last two digits is divisible by 4. For example, 6,248 is divisible by 4, but 6,250 is not. |

5 |
An integer is divisible by 5 if it ends in 0 or 5. |

6 |
An integer is divisible by 6 if it is even (divisible by 2) and also divisible by 3. Any even number divisible by 3 is also divisible by 6. |

8 |
A number is divisible by 8 if it is divisible by 2 three times, or if the last three digits are divisible by 8. For example, 24 is divisible by 8: 24÷ 2 = 12, 12 ÷ 2 = 6, 6 ÷ 2 = 3. For larger numbers, just check the last three digits. For example, 11,728 is divisible by 8 because 728 is divisible by 8 (728 ÷ 8 = 91). |

9 |
If the sum of the digits is divisible by 9, then the integer is divisible by 9. For example: 1,044 has digits that add to 9 (1 + 0 + 4 + 4 = 9) so 1,044 is divisible by 9 (1,044/9 =116). |

10 |
An integer is divisible by 10 if it ends in 0. |