## Divisibility by 7 and Its Proof

This is the 6th post in the Divisibility Rules Series. In this post, we discuss divisibility by 7.

Simple steps are needed to check if a number is divisible by 7. First, multiply the rightmost (unit) digit by 2, and then subtract the product from the remaining digits. If the difference is divisible by 7, then the number is divisible by 7.

**Example 1:** Is 623 divisible by 7?

3 x 2 = 6

62 – 6 = 56

56 is divisible by 7, so 623 is divisible by 7.

If after the process above, the number is still large, and it is difficult if to know if it is divisible by 7, the steps can be repeated. We take the difference as the new number, we multiply the rightmost digit by 2, and then subtract from the remaining digits.

**Example 2**: Is 3423 divisible by 7?

3 x 2 = 6

342 – 6 = 336

We repeat the process for 336. We multiply 6 by 2 and then subtract it from 33.

6 x 2 = 12

33 – 12 = 21

21 is divisible by 7, so 3423 is divisible by 7.

Note that if the number is still large, this process can be repeated over and over again, until it is possible to determine if the remaining digits is divisible by 7. » Read more