# Learn Divisibility Rules And How To Use Them

Division of numbers, particularly large ones, can be very difficult
without paper and pencil or calculator. There are tricks to simplify dividing numbers
- even large ones. We call these tricks Divisibility Rules or Rules Of Divisibility.

## Number Is Divisible By |
## If The Number Meets This Condition |
## Example |
---|---|---|

2 | If its last digit is 0, 2, 4, 6, or 8. | Examples: 12345678 is divisible by 2 because the last digit is 8.
12345678 ÷ 2 = 6172839. |

3 | If the sum of its digits are divisible by 3. | Example: 125172 is divisible by 3 because the sum of the digits is divided by 3.
1 + 2 + 5 + 1 + 7 + 2 = 18. 18 ÷ 3 = 6. |

4 | If its last two digits (taken together as a two-digit number) are divisible by 4. | Example: 1520 is divisible by 4 because the last two digit number pair (20) can
be divided by 4.
1520 ÷ 4 = 380. |

5 | If the number ends in 0 or 5. | Example: 875 is divisible by 5 because the last digit ends in 5.
875 ÷ 5 = 175. |

6 | It's even and the sum of its digits are divisible by 3. | Example: 1232718 is even because the last digit ends in 0, 2, 4, 6, or 8 - 8 in
this case.
Let's do check two; sum the digits and make sure they can be divided by 3. 1 + 2 + 3 + 2 + 7 + 1 + 8 is 24 and 24 ÷ 3 = 8. |

7 | This rule applies to three digit numbers only: the quantity "2 x (hundreds digit)
x ten's digit + (last digit)" is divisible by 7. |
Example: 710 is divisible by 7.
((2 × 7) × (1)) + 0 = (14 × 1) + 0 = 14. 14 ÷ 7 = 2. |

8 | If the last three digits (taken together as a three-digit number) are divisible by 8. | Example: 231912 is divisible by 8.
The last three digits are divisible 912 ÷ 8 = 114. If this is true, then 231912 ÷ 8 = 28989 must be true. |

9 | The sum of its digits is divisible by 9. |
Example: 18726354 is divisible by 9 because the sum of the digits is divisible by
9.
1 + 8 + 7 + 2 + 6 + 3 + 5 + 4 = 36. 36 ÷ 9 = 4. |

10 | If the number ends in 0. | Example: 1234567890 is divisible by 10 because the end digit is 0.
1234567890 ÷ 10 = 123456789. |