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. |

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