Divisibility Rule of 3 With Examples and FAQ – Mindspark

The divisibility rule of 3 is a shortcut method to test if a number is wholly divisible by 3 or not without performing any mathematical division process.

The divisibility rule of 3 

The divisibility rule of 3 says, “a number is divisible by 3 if the sum of all its digits is a multiple of 3 or wholly divisible by 3”. Let’s understand this with an example. 

Suppose we have to find if 234 is divisible by 3 or not. So we will add all the digits of 234, which will be 2 + 3 + 4 = 9. 

Now the sum 9 is a multiple of 3. Therefore, 234 is divisible by 3. 

The divisibility rule of 3 is helpful to check the divisibility in large numbers. Here, we keep applying the divisibility test until we get the sum of the digits of the number closer to 3 or multiple of 3. We follow the steps given below –

• First, add all the digits of the given number.
• Check if the sum is divisible by “3”. If it is still a large number, calculate it again.

• Check if the new sum is a multiple of 3. Repeat the above process if you are still not sure whether the sum of the digits is a multiple of 3 or not.

• If the final sum is a multiple of 3, we can confirm that the original number will be divisible by 3.

Example:  Let’s check if 23412 is divisible by 3 or not.

First, we calculate the sum of the digits, which is 2 + 3 + 4 + 1 + 2 = 12. 

The obtained sum of 12 is a multiple of 3. Therefore, 23412 would also be divisible by 3.

Similarly, we can check for 1121031. 

Adding all the digits, we get 1 + 1 + 2 + 1 + 0 + 3 + 1 = 9.

We know that 9 is divisible by 3. So, the original number 1121031 will also be divisible by 3.

Examples

1. Use the rule of divisibility of 3 to find out whether the large number 91682982 is divisible by 3 or not?

Using the rule of divisibility of 3, we will find the sum of all the digits of 91682982.

The sum will be 9 + 1 + 6 + 8 + 2 + 9 + 8 + 2 = 45. 

We are not sure if 45 is divisible by 3 or not. So, we will add both the digits of 45.

Now the final sum is 4 + 5 = 9, which is a multiple of 3.

Therefore 91682982 is divisible by 3.

2. Use the rule of divisibility of 3 and find out if the smallest three-digit number is divisible by 3 or not?

The smallest 3-digit number is 100. 

The sum of the digits of 100 is 1 + 0 + 0 = 2, which is not wholly divisible by 3.

Therefore, we can say that the smallest three-digit number is not divisible by 3.