Divisibility rules

Key Notes:

Divisibility by 2

  • Rule: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
  • Example: 24 is divisible by 2 because it ends in 4.

Divisibility by 3

  • Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
  • Example: For 123, the sum of the digits is 1 + 2 + 3 = 6, which is divisible by 3.

Divisibility by 4

  • Rule: A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
  • Example: For 312, the last two digits are 12, and 12 is divisible by 4.

Divisibility by 5

  • Rule: A number is divisible by 5 if its last digit is 0 or 5.
  • Example: 45 is divisible by 5 because it ends in 5.

Divisibility by 6

  • Rule: A number is divisible by 6 if it is divisible by both 2 and 3.
  • Example: 18 is divisible by 6 because it’s even (divisible by 2) and the sum of digits (1+8=9) is divisible by 3.

Divisibility by 7

  • Rule: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7 (including 0), then the original number is divisible by 7.
  • Example: For 203, double the last digit (6), subtract from the rest (20 – 6 = 14), and since 14 is divisible by 7, so is 203.

Divisibility by 8

  • Rule: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
  • Example: For 1,856, the last three digits are 856, and 856 is divisible by 8.

Divisibility by 9

  • Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.
  • Example: For 729, the sum of the digits is 7 + 2 + 9 = 18, and 18 is divisible by 9.

Divisibility by 10

  • Rule: A number is divisible by 10 if its last digit is 0.
  • Example: 50 is divisible by 10 because it ends in 0.

Divisibility by 11

  • Rule: A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.
  • Example: For 2728, sum of digits in odd positions (2 + 2 = 4) and sum of digits in even positions (7 + 8 = 15), difference is |4 – 15| = 11, which is divisible by 11.

Divisibility by 12

  • Rule: A number is divisible by 12 if it is divisible by both 3 and 4.
  • Example: For 144, since 144 is divisible by 3 (sum of digits is 9) and 4 (last two digits 44 are divisible by 4), it is divisible by 12.

Learn with an example

Is 77,619 divisible by 6?

  • yes
  • no

Try the “divisible by 6” rule on 77,619.

First check if 77,619 is divisible by 2.

Look at the ones digit:

77,619

The ones digit is 9. 

So, the number is not divisible by 2.

The rule says that 77,619 is not divisible by 6.

😀 Is 37,770,710 divisible by 10?

  • yes
  • no

Try the “divisible by 10” rule on 37,770,710.

Look at the ones digit:

37,770,710

The ones digit is 0. 

The rule says that 37,770,710 is divisible by 10.

Is 120 divisible by 6?

  • yes
  • no

Try the “divisible by 6” rule on 120.

First check if 120 is divisible by 2.

Look at the ones digit:

120

The ones digit is 0. 

So, the number is divisible by 2.

Now check if 120 is divisible by 3.

Find the sum of the digits:

1 + 2 + 0 = 3

3 is divisible by 3. So, the number is divisible by 3.
The rule says that 120 is divisible by 6.

let’s practice!