Divisibility Rule of 9 With Examples and FAQ – Mindspark

The divisibility rule of 9 is a shortcut trick to check if a number is divisible by 9 or not without performing the lengthy mathematical division process.

What is the Divisibility Rule of 9?

The divisibility rule of 9 has the same method as the divisibility rule of 3. In this rule also, we calculate the sum of the digits of the given number and check if the resultant number is 9 or a multiple of 9. If the resultant number is 9 or a multiple of 9, the number will be divisible by 9. Let us understand by an example.

Example – Let us check if the number 5526 is divisible by 9 or not.
Sum of digits of the given number = 5 + 5+ 2 + 6 = 18.
Since the resultant number (18) is a multiple of 9.
Hence, the number 5526 is divisible by 9.

Interesting Fact

If we again add the digits of the resultant number, we will find 9 as the new resultant number. Let us clear this statement with an example.

Example – We want to check if 653184 is divisible by 9 or not. 

Sum of digits = 6 + 5 + 3 + 1 + 8 + 4 = 27

Now again, add the digits of the resultant number 27.

So, the new resultant number = 2 + 7 = 9

Therefore, 653184 is divisible by 9.

Note – If the new resultant number again has more than one digit, add the digits again, and we will get 9.

Examples

1. Using the divisibility rule, find if 78990 is divisible by 9?

Solution:

First, we calculate the sum of the digits, which is 7 + 8 + 9 + 9 + 0 = 33

Again, we will add the digits 3 and 3, which is 3 + 3 = 6, and 6 is not a multiple of 9. 

Therefore, 78990 is not divisible by 9.

2. Which is the largest three-digit number completely divisible by 9?

Solution: We know that the largest three-digit number is 999. The sum of the digits is 9 + 9 + 9 = 27, a multiple of 9. Therefore, 999 is the largest three-digit number divisible by 9.