Divisibility Rule of 6 With Examples and FAQ – Mindspark

The divisibility rule of 6 is a combination of the divisibility rules of 2 and 3. It is a shortcut trick to know if a number is wholly divisible by 6 or not.

The divisibility rule of 6

The divisibility rule of 6 tells that a number is divisible by “6” if it is divisible by the numbers 2 and 3. It also means that all even multiples of 3 are divisible by 6. Let us see an example.

Suppose we want to check if 6312 is divisible by 6 or not.

The given number is an even number since the number’s last digit is 2 (an even number).

Now, check for the divisibility of 3. 

The sum of the digits is 6 + 3 + 1 + 2 = 12, which is a multiple of 3. So, 6312 is divisible by 3 also.

Therefore, 6312 is an even multiple of 3, and hence it will be divisible by 6.

For large numbers, we keep applying the divisibility test of 3 until we get the sum of the digits of the number closer to 3 or multiple of 3. Let’s take an example of a large number.

We want to know if 212268 is divisible by 6 or not. 

• The last digit of the number 212268 is an even number (8). So, we are sure that the number is divisible by 2.
• Adding all the digits of the number gives 2 + 1 + 2 + 2 + 6 + 8 = 21. The sum 21 is a multiple of 3, so 212268 will also be divisible by 3. 

(Note that the sum of the digits of the number 21 is 2 + 1 = 3 is also divisible by 3. We can repeat the addition process to get the sum closer to 3.)

• Since 212268 is divisible by 2 and 3 both. Therefore, we can confirm that it is divisible by 6.

Examples

1. Use the divisibility test of 6 and find out whether 24108 is divisible by 6?

The last digit of the number 24108 is an even number (8). So, we are sure that the number is divisible by 2.

Adding all the digits of the number gives 2 + 4 + 1 + 0 + 8 = 15. The sum 15 is a multiple of 3, so 24108 will also be divisible by 3.

Since 24108 is divisible by 2 and 3 both. Therefore, it is divisible by 6.

2. Find out if 36940 is divisible by 6?

The last digit of the given number 36940 is an even number (0). So, we are sure that the number is divisible by 2.

Adding all the digits of the number gives 3 + 6 + 9 + 4 + 0 = 22. The sum 22 is not a multiple of 3, so 36940 will not be divisible by 3.

Since 36940 is divisible by 2 but not by 3. Hence, it is not divisible by 6.