The Rules of Divisibility

The multiple of a number is always divisible by the number. The word “divisible” means that it can be divided exactly.

Example :

144 ÷ 4 = 36 (remainder = 0). So, 144 is divisible by 4 and is a multiple of 4.

144 ÷ 5 = 28 (remainder = 4). So, 144 is not divisible by 5 and is not a multiple of 5.

The following table gives criteria or conditions to test divisibility of any number by the numbers listed in the first column. This is useful when testing the divisibility of large numbers and to determine whether a number is a multiple of another.

Number Divisible by	Conditions	Examples
2	The last digit is an even number: 0, 2, 4, 6, 8	752, 300678, 890
3	The sum of all the digits of the number is divisible by 3.	5673 5+6+7+3 = 21 21 ÷ 3 = 7
4	The last two digits of the number is divisible by 4.	7624 24 ÷ 4 = 6
5	The last digit of the number is 0 or 5.	534,670 735
6	The sum of all the digits of the number is divisible by 3 and the last digit is zero or an even number.	8862 8+8+6+2 = 24 24 ÷ 3 = 8 last digit, 2, is even
7	Double the value of the last digit and subtract the result from the rest of the number. The answer is divisible by 7.	385 38 – (2 × 5) = 28 28 ÷ 7 = 4
8	The last three digits of a number is divisible by 8.	1800 800 ÷ 8 = 100
9	The sum of all the digits of the number is divisible by 9.	378 3 + 7 + 8 = 18 18 ÷ 9 = 2
10	The last digit is 0	8740

Example:

Check whether 171 is a multiple of 9.

Solution:

Sum of digits 1 + 7 + 1 = 9

9 ÷ 9 = 1

So, 171 is a multiple of 9

The following video describes the rules of divisibility

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