Smartick is a fun way to learn math! Feb01

# Divisibility Guidelines for 7 and Some Examples

How can we find out if a number is divisible by 7? In this post, we are going to look at the divisibility guidelines for the number 7.

One of the ways to find out is by dividing the number by 7. If the remainder is zero, we know that the number is divisible by 7. If the remainder is a number other than zero, the number is not divisible by 7.

But the following way is a faster way of checking:

To determine whether a number is divisible by 7, you have to remove the last digit of the number, double it, and then subtract it from the remaining number. If the remainder is zero or a multiple of 7, then the number is divisible by 7. If the remainder is not zero or a multiple of 7, the number is not divisible by 7.

It’s easier to understand if we look at an example:

## Is 1946 divisible by 7?

We separate the last digit:

194  6

Now we double the last digit and subtract it from the remaining number 194….. 2 x 6 = 12.

## 194 – 12 = 182

Since 182 is still a big number, we repeat the steps:

We separate the last digit:

18  2

We double the last digit and subtract it from the remaining number 18….2 x 2 = 4.

## 18 – 4 = 14

14 is a multiple of 7. Therefore 1946 is divisible by 7 because it follows the divisibility guidelines.

Easy, right? Let’s look at another example:

## Is 5219 divisible by 7?

We separate the last digit, double it, and subtract:

## 521 – 18 = 503

We repeat the same procedure:

## 50 – 6 = 44

44 isn’t a multiple of 7, therefore 5219 is not divisible by 7.  