How to Check if a Number is Divisible By 7?

The divisibility rule of 7 tells us if a number can be wholly divided by 7 without any remainder.

Usually, we know this with the division arithmetic process. But the divisibility rule of 7 has a shortcut trick to check the divisibility by 7 . Let’s see how.

Multiply the last digit by 2, and subtract the product from the remaining number to its left. If the difference is a 0 or a multiple of 7, we can confirm that the number is completely divisible by 7.

Example: Let us check if 392 is divisible by 7 or not? 

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. 

Divisibility Rule of 7 For Large Numbers

It is comparatively easy to check the divisibility of 7 for small numbers. However, for large numbers, we need to perform the divisibility test of 7.
In the case of larger numbers, we keep applying the divisibility test until we are sure that the number is divisible by 7.

Let us take a 6-digit number, 458416.

• First, we take the last digit of the number and multiply it by 2. So,(6 × 2 = 12). Subtract 12 from the rest of the number, which is 45841. So, 45841 -12 = 45829.  We are not sure if 45829 is a multiple of 7.
• We repeat the same process with 45829. Multiply the last digit by 2. So, (9 × 2 = 18). Subtract 18 from the rest of the number, So, 4582 – 18 = 4564. We are not sure if 4564 is a multiple of 7.
• Let us repeat the process with 4564. Multiply the last digit by 2. So, (4 × 2 = 8). Subtract 8 from the rest of the number, which is 456. So, 456 – 8 = 448. We are not sure if 448 is a multiple of 7.
• Let us repeat the process with 448. Multiply the last digit by 2. So, (8 × 2 = 16). Subtract 16 from the rest of the number, which is 44. So, 44 – 16 = 28, which is a multiple of 7. Therefore, we can confirm that 458416 is divisible by 7.  

Solved Examples

Q1: Using the divisibility rule, check if 195 is divisible by 7?

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.

Q2: 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 7.