Divisibility Rules are a set of rules which one can use while dividing numbers or to check if a particular number is divisible by another number or not. For example, in order to check if 729 is divisible by 9 or not, you can use the divisibility test of 9. If the sum of digits is divisible by 9 the number is also divisible by 9.

So in the above case 7 + 2+ 9 = 18, since 18 is divisible by 9 therefore 729 is also divisible by 9. Here we will provide you with all the details on the divisibility rules from 1 to 13 with examples.

Divisibility Rules Or Divisibility Tests

Divisibility tests or rules help you check the division of 2, 3, 4, 5..n digit numbers with other numbers. So in the next sections, we will provide you with the tests for the divisibility of numbers starting from 1 to 12.

These rules will help you perform the mathematical calculations with ease and score better marks. Since division is not limited to mathematics you can use these rules everywhere where division is involved.

Divisibility Rule of 1

Since every number irrespective of the type is divisible by 1 so there is no such rule to test the divisibility by 1.

Divisibility Rule of 2

All the even numbers or numbers ending with 2, 4, 6, 8, 0 are always divisible by 2. Example 4, 12, 28, 36, 50, 98008768.

Divisibility Rule of 3

For 3 we can say that if the sum of the digits is a multiple of 3, then the number is divisible by 3. Example 21 = 2+1 = 3 (hence divisible by 3), 35 = 3+5 = 8 (not divisible by 3).

Divisibility Rule of 4

A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4. Example 4612, here we will take the last 2 digits i.e. 12 and we all know that 12 is divisible by 4. Therefore, 4612 is also divisible by 4.

Divisibility Rule of 5

The divisibility rule for 5 is the easiest as you only have to look for numbers ending with 5 or 0. If a number ends with 0 or 5 it is divisible by 5 else not. Example 55787625760 is divisible by 5 and 5551 is not.

Divisibility Rule of 6

In this case, you have to consider the divisibility by both 2 and 3, and then we can say that if a number is divisible by 2 and 3 both then it is divisible by 6 also. Example 630 is divisible by both 2 and 3 because ending with 0 and 6+3+0 = 9. Hence also divisible by 6.

Divisibility Rule of 7

To check the divisibility by 7, you must first double the last digit and subtract it from a number made by the other digits. If the resulting number is divisible by 7, then the rule is valid. Example, 343 – following the rule double the last digit = 6 subtracting it from 34 – 6 = 28 and we know that 7 x 4 = 28. Hence, the rule follows.

Divisibility Rule of 8

A number with 4 or more digits is divisible by 8 if the number formed by the last three digits is divisible by 8. Example 1000, 2104, 1416, the last 3 digits are 000, 104, 416 and all these are divisible by 8.

Quick Note: The divisibility for numbers with 1, 2 or 3 digits by 8 has to be checked by actual division.

Divisibility Rule of 9

If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9. Example 5283 = 5+2+8+3 = 18 which is divisible by 9.

Divisibility Rule of 10

If a number has 0 in the ones place, then it is divisible by 10. Example 100, 198970, 1080.

Divisibility Rule of 11

This rule is a bit complicated, but with constant practice, you can easily implement this. First, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11. Example:

Divisibility Rule of 12

To be divisible by 12 a number must be divisible by both 3 and 4. Example 48 is divisible by both 3 and 4, hence also divisible by 12.

Divisibility Rules – Important Points to Remember

• i) If a number is divisible by another number, then it is divisible by each of the factors of that number.
• ii) If a number is divisible by two co-prime numbers, then it is divisible by their product also.
• iii) If two given numbers are divisible by a number, then their sum is also divisible by that number.
• iv) If two given numbers are divisible by a number, then their difference is also divisible by that number.

FAQs on Division Rules in Maths

Here are some questions that students generally search:

Q. If the sum of the digits of a number is divisible by 9, then the number will be divisible by a) 4 b) 3 c) 9 d) Both b & c Ans. d)

Q. Is there a divisibility rule for 7? Ans. Yes, as per the 7 divisibility test, you must double the last digit and subtract the number formed by the other two digits. For a detailed explanation with examples visit this page.

Q. What are the divisibility rules? Ans. Divisibility tests or rules are shorthand ways to determine whether a number is divisible by other numbers or not.

Q. What is the divisibility rule of 1 to 10? Ans. For 1 there is no divisibility test as all the numbers are divisible by 1. And, for 10, the numbers that end with 0 are divisible by 10.

So that was all on Divisibility Rules. We hope the information provided was fruitful. However, if you have further questions feel to use the comments section and we will update you at the earliest.