In this article, we will learn about divisibility rule of 7 with example. i.e. We will see how to check if any number is divisible by 7 or not.

What is Divisibility Rule of 7 ?

A number is divisible by 7 if the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0.

Example 1

Is 133 divisible by 7 or not?
Solution :

Double the unit digit = 3 x 2 = 6
Remaining part of the given number = 13.
According to divisibility rule of 7,
The difference between twice the unit digit and remaining part of the given number is multiple of 7 or equal to 0 or not.
13 – 6 = 7
Thus, the difference between twice the unit digit and the remaining part of the given number is 7,  which is divisible by 7.
So, the given number 133 is divisible by 7.

Example 2

Check if 438 is divisible by 7 or not.
Solution:

Double the unit digit = 8 × 2 = 16.
Remaining part of the given number = 43
We need to check the difference between twice the unit digit and remaining part of the given number is multiple of 7 or equal to 0 or not.
43 – 16 = 27.
Thus, the difference between twice the unit digit and the remaining part of the given number is 27, which is  not divisible by 7.
So, the given number 438 is not divisible by 7.

Example 3

Is 105 divisible by 7 ?
Solution:

Double the unit digit = 5 × 2 = 10.
Remaining part of the given number = 10
We need to check the difference between twice the unit digit and remaining part of the given number is multiple of 7 or equal to 0 or not.
10 – 10 = 0
Thus, the difference between twice the unit digit and the remaining part of the given number is equal to 0.
So, the given number 105 is divisible by 7.

Example 4

Is 705 divisible by 7 ?
Solution:

Double the unit digit = 5 × 2 = 10.
Remaining part of the given number = 70
We need to check the difference between twice the unit digit and remaining part of the given number is multiple of 7 or equal to 0 or not.
70 – 10 = 60
Thus, the difference between twice the unit digit and the remaining part of the given number is 60, which is not divisible by 7.
So, the given number 705 is not  divisible by 7.