Divisibility Rules With Examples and FAQ – Mindspark

What are Divisibility Rules or Divisibility Tests?

We use divisibility rules or tests to check whether the given number is wholly divisible by another number. Suppose we want to know if 8034160 is divisible by 5 or not?

To check this, you have two methods – the first is to go through a lengthy mathematical division process (time taking), and the second is to apply the divisibility rule (time-saving).

So, we can conclude that divisibility tests help us to solve lengthy mathematical calculations quickly. In this article, we will learn about the divisibility rules from the number 2 to 12.

Divisibility Rules From 2 to 12

The divisibility test of 1 is not required since every number is divisible by 1. So we start with the divisibility rule of 2.

Divisibility Rule of 2

Every even number is divisible by 2. Any number with 0, 2, 4, 6 or 8 at the ones place is an even number and thus divisible by 2.

Divisibility Rule of 3

A number is divisible by 3 if the sum of the digits of that number is 3 or a multiple of 3, i.e. 6, 9, 12, 15 etc. 

Example – 348 is divisible by 3, as the sum of all the digits is 3 + 4 + 8, which is 15, and 15 is a multiple 3. So, 348 is divisible by 3. 

Divisibility Rule of 4

If a number’s last two digits form a number that is divisible by 4 or is 00, the number will be divisible by 4.

Example – 572 will be divisible by 4 because the number formed by the last two digits is 72, which is divisible by 4.

Similarly, 900 will also be divisible by 4 since the last two digits make 00.

Divisibility Rule of 5

All those numbers that have 0 or 5 as the last digit are divisible by 5.

Example – 525, 1200 since they have 5 and 0 as their last digits, respectively.

Divisibility Rule of 6

If a number is divisible by 2 and 3, that number will be divisible by 6 also.

Example – 354 divisible by 6. The sum of all the digits of 354 is 12, so it is divisible by 3. The last digit is 4, so it is divisible by 2 also. Hence it is divisible by 6.

Divisibility Rule of 7

For a number to be divisible by 7, subtracting twice the last digit of the number from the remaining digits should be divisible by 7.

Example –  364 is divisible by 7 as when we subtract the twice of the ones place digit, 

4 × 2 = 8, and subtracting it from the remaining digits 36, we get 36 – 8 = 28, which is divisible by 7. So, 364 is divisible by 7.

Divisibility Rule of 8

If a number’s last three digits form a number that is divisible by 8 or is 000, the number will be divisible by 4.

Example – 79240 is divisible by 8, as the number formed by the last three digits 240 is completely divisible by 8. 

Similarly, 3000 will be divisible by 8 since the last three digits make 000.

Divisibility Rule of 9

A number is divisible by 9 if the sum of the digits of that number is 9 or a multiple of 9, i.e. 9, 18, 27, 36, 45 etc. 

Example – 873 will be divisible by 9 because the sum of digits 8 + 7 + 3 = 18 is divisible by 9.

Divisibility Rule of 10

All those numbers that have zero as the last digit are divisible by 10.

Example – 20, 30, 100, 5000, 60000, etc., are divisible by 10 since the last digit is zero.

Divisibility Rule of 11

For a number to be divisible by 11, the difference of the sums of the alternative digits of a number should be zero or a multiple of 11.

Example – 1331 is divisible by 11 because the sum of digits at odd places 1 + 3 = 4 and sum of digits at even places 3 + 1 = 4 and their difference 4 – 4 = 0.

Divisibility Rule of 12

If a number is divisible by 3 and 4, that number will be divisible by 12 also.

Example – 1848 is divisible by 12 since it is divisible by both 3 and 4.

Examples: 

1. Check if 354 is divisible by 3?

Sum of digits = 3 + 5 + 4 = 12 which is divisible by 3.

Therefore, 354 is divisible by 3. 

2. Check if 732 is divisible by 4 or 9?

The number formed by the last 2 digits is 32, which is divisible by 4.

Sum of digits = 7 + 3 + 2 = 12 which is not divisible by 9.

Therefore, 732 is divisible by 4.