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:

- Take the last digit of the number and multiply it by 4.
- Remove the last digit from the number.
- Subtract the result obtained in step 1 from the number obtained in step 2.
- 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.

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