What is a divisibility test? Definition and examples

A divisibility test is a rule used to find out if a number can be divided by another number without doing long division. Usually, we perform the test in order to see if a number can be divided by 2, 3, 4, 5, 6, 9, and 10.

Divisibility by 2

A number is divisible by 2 if the digit in the ones place is even (ends in 0, 2, 4, 6, or 8)

For example, 4536 is divisible by 2 since the digit in the ones place is 6 and 6 is even.

Divisibility by 3

A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

For example, 4536 is divisible by 3 since 4+5+3+6 = 18 and 18 is divisible by 3.

Divisibility by 4

A number is divisible by 4 if the number formed by the digit in the tens place and the digit in the ones place is divisible by 4.

For example, 4536 is divisible by 4 because 36 is divisible by 4

Divisibility by 5

A number is divisible by 5 if the digit in the ones place is 0 or 5.

For example, 4530 is divisible by 5 since the digit in the ones place is 0.

Divisibility by 6

A number is divisible by 6 if the number is divisible by both 2 and 3.

For example, 4536 is divisible by 6 since it is divisible by both 2 and 3.

Divisibility by 9

A number is divisible by 9 if the sum of the digits of the number is divisible by 9.

For example, 4536 is divisible by 9 since 4+5+3+6 = 18 and 18 is divisible by 9.

Divisibility by 10

A number is divisible by 10 if the digit in the ones place is 0.

For example 4530 is divisible by 10 since the digit in the ones place is 0.