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Divisibility Rules

It is easy to check if a number can be evenly divided by the numbers from 1 to 10.

Here is a list of the disibility rules.

Evenly Division by 2

A number can be evenly divided by 2, if the last digit of the number is an even number.

For example:

1734 can be evenly divided by 2, because the last digit, 4, is an even number.

1143 cannot be evenly divided by 2, because the last digit, 3, is an odd number.

Evenly Division by 3

A number can be evenly divided by 3, if checksum of the number can be evenly divided by 3.

For example:

Can 1734 be divided evenly by 3?

The checksum of 1734 is 1 + 7 + 3 + 4 = 15
The checksum of 15 is 1 + 5 = 6.

Since the checksum, 6, can be evenly divided by 3, 1734 can be evenly divided by 3.

Evenly Division by 4

A number can be evenly divided by 4, if the number’s last two digits can be evenly divided by 4.

For example:

8412 can be evenly divided by 4, because 12 can be divided evenly by 4.

13765 cannot by divided evenly by 4, because 65 cannot be divided evenly by 4.

Evenly Division by 5

A number can be divided evenly by 5, if it’s last digit is either 0 or 5.

For example:

635 can evenly be divided by 5, because the last digit of the number is 5.

817 cannot be divided evenly by 5, because the last digit of the number is not 0 or 5.

Evenly Division by 6

A number can be divided evenly by 6, if the number can be divided evenly by 3 and if it is an even number.

Evenly division by 7

This is a bit more complicated.

To check if a number can be evenly divided by 7, the first thing you do is to remove the last digit of the number, multiply the digit by two and subtract the result from the rest of the number’s digits. This process is repeated until the number is small enough to check if it can be evenly divided by 7.

For example:

Can 6258 be divided evenly by 7?

We remove 8 and multiply 8 by 2, the result of which is 16.

We subtract 16 from the rest of the number’s digits, 625:

625 - 16 = 609

We remove 9, multiply it by 2, and subtract the result from the rest of number’s digits:

60 - 18 = 42

We know that 42 can be evenly divided by 7.

So 6258 can be divided evenly by 7.

Evenly Division by 8

A number can be evenly divided by 8, if the last three digits of the number can be evenly divided by 8.

For example:

78512 can be evenly divided by 8, because 512 can be evenly divided by 8.

33036 cannot be divided evenly by 8, because 036 (or just 36) cannot be divided evenly by 8.

Evenly Division by 9

A number can be evenly divided by 9 if the checksum of the number can be divided evenly by 9.

For example:

4923 can be evenly divided by 9, because the checksum is 4 + 9 + 2 + 3 = 18, and 18 can be divided evenly by 9.

123 cannot be divided evenly by 9, because the checksum is 1 + 2 + 3 = 6, and 6 cannot be divided evenly by 9.

Evenly Division by 10

A number can be evenly divided by 10, if the last digit of the number is 0.

For example:

720 can be divided evenly by 10, because the last digit of the number is 0.

775 cannot be divided evenly by 10, because the last digit of the number is not 0.

Check if a number can be evenly divided by the numbers from 1 to 10.

Number: