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Divisibility Rule of 2, 3, 4, 5, 6, 7, 8, 9, 10 | Short Trick for Divisibility



Rule of Check Whether a Number is Divisible by 2:

A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.

Example: 66 is divisible by 2 since the last digit is 6.


Rule of Check Whether a Number is Divisible by 3:

A number is divisible by 3 if the sum of the digits is divisible by 3.

Example: 198 is divisible by 3 Since the sum of the digits is 18 (1 + 9 + 8 = 18), and 18 is divisible by 3.


Rule of Check Whether a Number is Divisible by 4:

A number is divisible by 4 if the number formed by the last two digits is divisible by 4.

Example: 516 is divisible by 4 since 16 is divisible by 4.


Rule of Check Whether a Number is Divisible by 5:

A number is divisible by 5 if the last digit is either 0 or 5.

Example: 285 is divisible by 5 since the last digit is 5.


Rule of Check Whether a Number is Divisible by 6:

A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3.

Example: 198 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.


Rule of Check Whether a Number is Divisible by 7:

To check if the number is divisible by 7 or not. Follow the following steps.

Step 1: Take the last digit of the number and double it.

Step 2: Subtract this number from the rest of the digits in the original number.

Step 3: If this new number is either 0 or if it’s a number that’s divisible by 7, then the original number is also divisible by 7. If you can’t easily tell yet if the new number is divisible by 7, go back to the first step with this new smaller number and try again.


Example: Let us understand whether 2033 is divisible by 7

Step 1: The last digit of 2023 is 3, so double it i.e. 3 X 3 = 6

Step 2: Subtract 6 from the remaining digit from the original number i.e. 202 which gives us 202 – 6 = 196.

Step 3: Is 196 divisible by 7. If you are not sure then repeat the steps using the new number 196.

Step 4: The last digit of 196 is 6, so double it i.e. 6 X 2 = 12

Step 5: Subtract 12 from the remaining digit from the new number i.e. 19 which gives us 19 – 12 = 7.

Since, 7 is divisible by 7 so the number 2023 is divisible by 7.


Rule of Check Whether a Number is Divisible by 8:

A number is divisible by 8 if the number formed by the last three digits is divisible by 8.

Example: 7,128 is divisible by 8 since 128 is divisible by 8.


Rule of Check Whether a Number is Divisible by 9:

A number is divisible by 9 if the sum of the digits is divisible by 9..

Example: 198 is divisible by 9 since the sum of the digits is 18 (1 + 9 + 8 = 18), and 18 is divisible by 9.


Rule of Check Whether a Number is Divisible by 10:

A number is divisible by 10 if the last digit is 0.

Example: 7,770 is divisible by 10 since the last digit is 0.


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