# Divisibility criteria

**Divisibility criteria** are practical rules that are useful to find out if a number is divisible by 2, 3, 5 or 11.

One number is *divisible by 2* if it is even. Example: 234458 is divisible by 2.

One number is *divisible by 3* if the result of the addition of its digits is divisible by 3.

Example: 1593 is divisible by 3 because 1 + 5 + 9 + 3 =18 is divisible by 3

One number is *divisible by 5* if the units’ digit is 0 or 5.

Example: 12345 is divisible by 5

One number is *divisible by 11* if we add the even position digits and, separately, the odd position digits and, when we subtract the results, we obtain 0 or a multiple of 11.

Example: 1358808 is divisible by 11 because 1 + 5 + 8 + 8 = 22 and 3 + 8 + 0 = 11 and 22 - 11 = 11 which is a multiple of 11

In the other cases (7,13,17,...) you have to do the division.

**Exercise**: complete this table:

... is divisible by |
2 |
3 |
5 |
11 |

54.321 | ||||

555.555 | ||||

5.555.555 | ||||

23.456.780 | ||||

103.070.803 |

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