7 Divisibility Rule with Examples and FAQs

What is the divisibility rule of 7?

A method to find out that any given number is divisible by 7 without actually dividing the number by 7 is the 7 Divisibility rule.

The steps to check the divisibility are:

• The digit at the unit’s place of the given number is multiplied by 2.
• The result of the multiplication is then subtracted from the remaining part of the number.
• If the difference is a multiple of 7 or 0, then we can say that the number is divisible by 7.

By looking at the multiples of 7, for example, 7, 14, 21, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, etc., we know which numbers are divisible by 7.

Now let us consider a 3-digit number, 259.

The last digit of the number is 9, now 2 × 9 = 18.

The remaining part of the number 259, is 25. Subtracting 18 from 25 and checking if the result is divisible by 7.

25 – 18 = 7, which is 7 itself.

Hence, 259 is divisible by 7 which has been checked by the 7 divisibility rule. 

This was easy as the number was small. Now, what should be done if a bigger number is given?

Within 3 steps it cannot be determined if the number is divisible by 7 or not. For that, we keep on repeating the steps till we get closer to a number about which we are sure to be divisible by 7.

Let us consider a large number, 19915.

The last digit of the number is 5, now 2 × 5 = 10.

The remaining part of the number 19915, is 1991. Subtracting 10 from 1991 and checking if the result is divisible by 7.

1991 – 10 = 1981, 

Which is a large number and we don’t know it is divisible by 7, so we repeat the steps from the first step. This time we take 1981 as the number.

The last digit of the number is 1, now 2 × 1 = 2.

The remaining part of the number 1981, is 198.

Subtracting 2 from 198 and checking if the result is divisible by 7.

198 – 2 = 196, 

Again, we don’t know it is divisible by 7, so we repeat the steps from the first step. This time we take 196 as the number.

The last digit of the number is 6, now 2 × 6 = 12.

The remaining part of the number 196, is 19.

Subtracting 12 from 19 and checking if the result is divisible by 7.

19 – 12 = 7, which is 7 itself. 

Hence, 19915 is divisible by 7 which has been checked by the divisibility test.

Examples

Example 1: Using the divisibility rule of 7, can you determine if 36687 is divisible by 7?

Solution:

The last digit of the number 36687 is 7.

To double the last digit, we multiply it by 2 i.e., 7 × 2 = 14.

14 is subtracted from the remaining number that is 3668.

3668 – 14 = 3654

Repeating the steps again because if 3654 is divisible by 7 is not known.

The last digit of the number is 4.

To double the last digit, we multiply it by 2 i.e., 4 × 2 = 8.

8 is subtracted from the remaining number that is 365.

365 – 8 = 357

Again, the steps are repeated because if 357 is divisible by 7 is not known.

The last digit of the number is 7.

To double the last digit, we multiply it by 2 i.e., 7 × 2 = 14.

14 is subtracted from the remaining number that is 35.

35 – 14 = 28

28 = 7 × 4, hence we can say that 36687 is divisible by 7.

Example 2: Rita has 343 stickers in her collection, she wants to arrange the stickers in such a manner that there are 7 stickers in one row. Check by divisibility test if it is possible to do so without any row being left incomplete.

Solution:

To check if it is possible to arrange 343 stickers in a row of 7 we use the divisibility rule of 7.

The last digit of the number 343 is 7.

To double the last digit, we multiply it by 2 i.e., 3 × 2 = 6.

6 is subtracted from the remaining number that is 34.

34 – 6 = 28

28 = 7 × 4, hence we can say that 343 is divisible by 7.

Rita can arrange her stickers in such a manner that each row contains 7 stickers without any row being incomplete.