divisible by | Rules | Example |
---|---|---|

2 | All even numbers are divisible by 2. Ex., all numbers ending in 0,2,4,6 or 8. |
1234 - Divisible by 2 1237 - Not divisible by 2 |

3 |
Add up all the digits in the number. If the sum is divisible by 3 then the number is also divisible by 3. |
Is 23457 divisible by 3? 1) 2 + 6 + 4 + 5 + 7 = 24; 2) 24: 2 + 4 = 6 3) 6 is divisible by 3; so 23457 is also divisible by 3 |

4 |
If the last 2 digits of a number is divisible by 4 then the number also divisible by 4 |
12320: Last 2 digits (20) is divisible by 4, So 12320 is also divisible by 4. |

5 | If the last digit is a 5 or a 0, the number is divisible by 5. |
4590: number ends with 0; 3265: number ends with 5 So both are divisible by 5. |

6 |
If the number is divisible by 2 and 3 then it is divisible by 6 also. Apply divisibility rule of 2 and 3. |
2568 is divisible by 6 because it is divisible by 2 and 3. 1) Last digit (8) is even. So divisible by 2 2) sum of all digits: 2 + 5 + 6 + 8 = 21 3) 2 + 1 = 3 (3 is divisible by 3) |

7 |
Double the last digit and subtract it from the rest of the number. If the answer is divisible by 7 (or 0) then it is divisible by 7 This rule can be applied until the result is small enough to divide by 7. |
Is 16184 divisible by 7? 1) 1618 - (2 * 4) = 1610 2) 161 - (2 *0) = 161 3) 16 - 2 = 14 4) 14 is divisible by 7. So 16184 is also divisible by 7. |

8 |
If the last three digits of the number is divisible by 8 then the entire number is divisible by 8. The following rule can be used for quick elimination. Apply divisibility rule of 2 and 4, If it fails then the number can not be divided by 8. |
Is 18512 is divisible by 8? Last 3 digits of 18512 is 512. 512 is divisible by 8. So 18512 is divisible by 8. |

9 |
Add up all the digits in the number. If the sum is divisible by 9 then the number is also divisible by 9. |
11916 divisible by 9 1) 1 + 1 + 9 + 1 + 6 = 18 2) 1 + 8 = 9 3) 9 is divisible by 9. |

10 | If the last digit of the number is 0 then the number is divisible by 10. |
23760: Last digit is 0 so it is divisible by 10. 34561: Last digit is not 0 so it is not divisible by 10. |

11 |
Alternately add and subtract the digits from left to right. (Assume 0 is added to the first digit.) If the result (including 0) is divisible by 11, the number is also. |
365167484 is divisible by 11, start by subtracting:
[0+]3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11. |

12 |
The number is divisible by both 3 and 4 then the number is divisible by 12. Apply divisibility rule of 3 and 4. |
2772 divisible by 12 because it is divisible by 3 and 4. 1) 2 + 7 + 7 + 2 = 18 ; 1 + 8 = 9. 9 is divisible by 3 2) last two digits of 2772 = 72. 72 is divisible by 4 |