In this article, we will learn about divisibility rule of 3 with example. i.e. We will see how to check if any number is divisible by 3 or not.

What is Divisibility Rule of 3 ?

A number is divisible by 3 if the sum of all digits of that number is divisible by 3 or multiple of 3.

Example 1

Check if 128 is divisible by 3 or not.

Solution:

We need to find sum of all digits of 128. Digits in 128 are 1, 2 and 8.

So, sum of digits of 128  = 1 + 2 + 8 = 11`

Now, 11 is not divisible by 3. So, 128 is not divisible by 3.

Example 2

Check if 192 is divisible by 3 or not.

Solution:

We need to find sum of all digits of 192. Digits in 192 are 1, 9 and 2.

So, sum of digits of 192  = 1 + 9 + 2 = 12

Now, 12 is divisible by 3. So, 192 is divisible by 3.

Example 3

Is 34561949 is divisible by 3 ?

Solution:
Sum of digits are  = 3 + 4 + 5 + 6 + 1 + 9 + 4 + 9 = 41
41 is not divisible by 3. So, 34561949 is NOT divisible by 3.

Example 4

Fill the lowest possible digit in the blank space so that number is divisible by 3.

1. 4569_
   Solution: As per divisibility rule of 3, any number is divisible by 3 if sum of all the digits of that number is divisible by 3.
   So, Sum of digits of 4569_ is = 4 + 5 + 6 + 9 + _
   24 + _ . Now, 24 is divisible by 3. So, possible digits in place of _ can be 0, 3, 6 and 9. Here, 0 is smallest . So, correct answer is 0. Thus, number will be 45690.
2. 875_2
   Solution: As per divisibility rule of 3, any number is divisible by 3 if sum of all the digits of that number is divisible by 3.
   So, Sum of digits of 875_2 is = 8 + 7 + 5  + _ + 2
   22 + _ . Now, 22 is not divisible by 3. Next largest number that is divisible by 3 is 24. So, if we add 2 in 22, it will be 24. We need to fill 2 in blank space to make number divisible by 3.
   Thus, final number is 87522.

Example 5

Using divisibility rule of 3, check if the largest 4 digits number is divisible by 3 or not.

Solution:
Largest 4 digits number is 9999
By divisibility rule of 3, any number is divisible by 3 if the sum of all digits of that number is divisible by 3.
So, Sum of all digits of 9999 = 9 + 9 + 9 + 9 = 36.
Now, 36 is divisible by 3. So, 9999 is divisible by 3.
Hence, Largest 4 digits number is divisible by 3.

If you want to know more about digit 3, visit here