Divisible By 7 – Divisibility Rule, Examples and FAQs

A number is divisible by 7 if it leaves zero as the remainder when divided by 7. Here we will learn the divisibility rule of 7 and understand it with examples.

How to Check if a Number is Divisible By 7?

The divisibility rule of 7 helps us to know if a number is completely divisible by 7 or not without performing a lengthy mathematical division process. Let us see this shortcut trick.

Multiply the last digit of the given number by 2, and subtract the product from the remaining number to its left. If the difference is zero or a multiple of 7, the given number is completely divisible by seven. Now let us check a number for the divisibility by 7.

Let us apply this rule to the number 392.

Last digit of the number = 2.

Multiply it by 2, and we get 2 × 2 = 4.

Rest of the number = 39.

Now subtracting 4 from 39, we get 39 – 4 = 35, a multiple of 7.

Therefore, 392 is divisible by 7. 

In the case of large numbers, we keep applying the divisibility test repeatedly until we are sure that the number is a multiple of 7.

Let us check the divisibility by 7 for the number 460131.

First, we multiply the last digit of the number by 2. 

The last digit of the number 460131 is 1. On doubling it, we get (1 × 2 = 2). 

Now subtract 2 from the rest of the number to the left of the last digit, which is 46013. So, 46013 -2 = 46011. 

We are not sure if 46011 is a multiple of 7.

So we repeat the above process for 46011. Multiply the last digit by 2. 

The last digit of the number 46011 is 1. On doubling it we get (1 × 2 = 2). 

Now subtract 2 from the rest of the number, So, 4601 – 2 = 4599. We are still not sure if 4599 is a multiple of 7 or not.

Now repeat the same process with 4599.  This time we get 441. We are again not sure if 441 is a multiple of 7 or not.

Once again, repeat the process with 441.  This time we get 42 as our answer that is a multiple of 7. 

Therefore, we can say that 460131 is divisible by seven.  

Examples

1. Apply the divisibility rule of 7 to the number 195.

Solution :

Last digit of the number = 5.

Multiplying it by 2 gives 5 × 2 = 10.

Remaining Number = 19.

Subtracting 10 from 19 gives 19 – 10 = 9, which is not a multiple of 7.

Therefore, 195 is not divisible by 7.

2. Check if 2457 is divisible by 7 using the divisibility test of 7?

Solution :  

Last digit of the number = 7.

Multiplying it by 2 gives 7 × 2 = 14.

Remaining Number = 245.

Subtracting 14 from 245 gives 245 – 14 = 231; we are not sure if it is a multiple of 7 or not.

So, repeat the process for 231.

Last digit of the number = 1.

Multiplying it by 2 gives 1 × 2 = 2.

Remaining Number = 23.

Subtracting 2 from 23 gives 23 – 2 = 21, which is a multiple of 7.

Therefore, 2457 is divisible by seven.