In this article, we will learn about divisibility rule of 13 with example. i.e. We will see how to check if any number is divisible by 13 or not.

What is Divisibility Rule of 13 ?

To check if a number is divisible by 13, we can use the following rule:

1. Take the last digit of the number and multiply it by 4.
2. Remove the last digit from the number.
3. Subtract the result obtained in step 1 from the number obtained in step 2.
4. Repeat steps 1-3 until a result is obtained that is either divisible by 13 or less than 13.

If the final result is 0 or a multiple of 13, then the original number is divisible by 13.

Example 1

Check if 416 is divisible by 13 or not.
Solution:

In the given number 416, last digit is 6. Multiplying the last digit by 4, we get (4 × 6), which is 24.
Adding 24 to the rest of the digits in the given number, we get 41 + 24 = 65.
Since 65 is a multiple of 13, 416 is divisible by 13.

Example 2

Check if 793 is divisible by 13 or not.
Solution:

In the given number 793, last digit is 3. Multiplying the last digit by 4, we get (4 × 3), which is 12.
Adding 12 to the rest of the digits in the given number, we get 79 + 12 = 91.
Since 91 is a multiple of 13, 793 is divisible by 13.

Example 3

Is  173 divisible by 13 ?
Solution:

In the given number 173, last digit is 3. Multiplying the last digit by 4, we get (4 × 3), which is 12.
Adding 12 to the rest of the digits in the given number, we get 17+ 12 = 29.
Since 29 is not divisible by 13, 173 is not divisible by 13.

Example 4

Is 50674 is divisible by 13?
Solution:

In the given number 50674, last digit is 4. Multiplying the ones place digit by 4, we get (4 × 4), which is 16.
Adding 16 to the rest of the digits in the given number, we get 5067 + 16 =5083.
Now, we will check again if 5083 is divisible by 13 or not.

Again,
Four times of the last digit of 5083 = 4  x 3 = 12.
Now, adding 12 to the rest of digits in the given number, we get 508 + 12 =520.
Now, we will check again if 520 is divisible by 13 or not.

Again,
Four times of the last digit of 520 = 4 x 0 = 0.
Now, adding 0 to the digits in the given number, we get 52 + 0= 52.
Since 52 is divisible by 13 (i.e. 13 x 4 = 52), 50674 is divisible by 13.