Divisibility Tests

Divisibility rules of whole numbers are very useful because they help us to quickly determine if a number can be divided by 2, 3, 4, 5, 9, and 10 without doing long division. This is especially useful when the numbers are large.

Divisibility Rule of 1

Any integer that is not a fraction is divisible by 1.

Eg:- 23, 84, 974, 1023

Divisibility Rule of 2

If a number is an even number or a number whose last digit is an even number.

Eg:-  0, 2, 4, 6, 8, 10

Divisibility Rule of 3

When the sum of all digits of a number is a multiple of 3.

Eg:- 516, 36, 119, 5502

Divisibility Rule of 4

The number formed by last 2 digits is divisible by 4.

Eg:- 92, 780, 52, 300

Divisibility Rule of 5

When the ones digit of the number is either 0 or 5.

Eg:- 55, 125, 1000, 760

Divisibility Rule of 6

A number is divisible by 6 if it is divisible by 2 and 3 also.

Eg:- 270, 630, 144, 42

Divisibility Rule of 7

When the difference between twice the digits at ones place and the number formed by other digit is either zero or a multiple of 7.

Eg:- 1073, 98, 56, 140

Divisibility Rule of 8

The number formed by last 3 digits is divisible by 8.

Eg:- 1792, 1824, 2000, 2880

Divisibility Rule of 9

When the sum of all digits of a number is a multiple of 9.

Eg:- 51984, 2979, 9000, 135

Divisibility Rule of 10

When the ones digit is zero.

Eg:- 1000, 150, 670, 280