Divisibility Tips and Tricks

Following table is the best way to understand the shortcut of the divisibility rules from 2 to 10,

Divisibility Rule of 11 

To check the divisibility rule for 11, if the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.

Example: Let us consider a number to test the divisibility with 11, 264482240 mark the even place values and odd place values. Sum up the digits in even place values together and sum up the digits in odd place values together.                        

Now sum up the digits in even place values i.e., 0^th + 2^th + 4^th + 6^th + 8^th = 2 + 4 + 8 + 2 + 0 = 14. To add up the digits in odd place values i.e., 1^th+ 3^th + 5^th + 7^th = 6 + 4 + 2 + 4 = 14

Now calculate the difference between the sum of digits in even place values and the sum of digits in odd place values if the difference is divisible by 11 the complete number i.e., 264482240 is divisible by 11. Here the difference is 0, (14-14) which is divisible by 11. Therefore, 264482240 is divisible by 11.

Divisibility Rule of 12

For any number to be divisible by 12, it must be divisible by 3 as well as 4 simultaneously. So, the divisibility rule of 3 and 4 is used together to check whether a number is divisible by 12 or not. 

For example, let’s check whether 3276 is divisible by 12 or not.

Divisibility by 3, 3 + 2 + 7 + 6 = 18, which is divisible by 3.

Thus 3276 is divisible by 3.

As 76 is the last two digits of 3276, and 76 is divisible by 4 (76 = 4×19).

Thus, 3276 is divisible by 4 as well.

As 3276 is divisible by 3 and 4 simultaneously, thus 3276 is divisible by 12 as well.

Note: For all the composite numbers such as 14, 16, 18, 20, etc., we can check their divisibility using the divisibility rule of their constituents factors.

Divisibility Rule For 13

To check, if a number is divisible by 13, add 4 times the last digit to the rest of the number and repeat this process until the number becomes two digits. If the result is divisible by 13, then the original number is divisible by 13.

Example: Check whether 333957 is divisible by 13 or not.

Solution:

Unit digit of 333957 is 7,

(4 × 7) + 33395 = 33423

(4 × 3) + 3342 = 3354

(4 × 4) + 335 = 351

(1 × 4) + 35 = 39

(1 × 4) + 35 = 39

Reduced to two-digit number 39 is divisible by 13. 

Therefore, 33957 is divisible by 13.

Divisibility Rule of 17 

A number is divisible by 17, when dividing it by 17 there is no remainder left. To check, if a number is divisible by 17, subtract 5 times the last digit from the rest of the number and repeat this process until the number becomes two digits.

If the result is divisible by 17, then the original number is also divisible by 17.

 Example: Is 28730 divisible by 17 or not?

Solution:

Unit digit of 28730 is 0,

2873 – (5 × 0) = 2873

287 – (5 × 3) = 272

27 – (5 × 2) = 17

Reduced to two-digit number 17 is divisible by 17. 

Therefore, 28730 is divisible by 17.

Divisibility Rule of 19

To check, if a number is divisible by 19, take its unit digit and multiply it by 2, then add the result to the rest of the number, and repeat this step until the number is reduced to two digits.

If the result is divisible by 19, then the original number is also divisible by 19. Otherwise, the original number is not divisible by 19.

 Example: Is 12635 divisible by 19 or not?

Solution:

Unit digit of 12635 is 5,

1263 + (2× 5) = 1273

127 + (2 × 3) = 133

13 + (2 × 3) = 19

Reduced to two-digit number 19 is divisible by 19. 

Therefore, 12635 is divisible by 19.

Also, Read:

• Class 8 Maths Notes for Divisibility Rules
• Class 8 Maths NCERT Solutions for Divisibility Rule
• RD Sharma Class 8 Solutions for Divisibility Rules

Divisibility Rules are the tests that were developed to make the division process simple and quicker. If we have to check whether a number is divisible by some other number, we can use these rules and check the same without the long division method.

Let’s learn what are divisibility tests in mathematics and their rules in detail.