Divisibility rule of 7 explained with examples

Learn and know divisibility rule of 7 which is not known by most of us. Do you know the first thing that we will get in the mind, when someone asks what is the divisibility rule for the number 7? We definitely say that there is no any divisibility rule for the number 7? Because in our school days they said that there is no divisibility rule of 7. Except divisibility rule of 7 remaining we will learn i.e. divisibility rule of 4, divisibility rule of 9, and divisibility rule of 6 and so on.Divisibility rule of 7 explained with examples

At first I also thought really there is no divisibility rule for 7. But the fact is, there is a divisibility rule for 7. What I know about divisibility rule of 7, am sharing with you. So go through it, it will be useful to you. To be frank, there are so many divisibility rules for 7 exists, but in all these the below given method is simple and easy to do.  

Below given are the steps for divisibility rule of 7:

Step 1:

In the given number, Double the unit digit and subtract it from remaining number.

Step 2:

Now see the result is divisible by 7 or not. If the result is a big number, again two times (double) of unit digit subtract from remaining number.

One again check the obtained result is divisible by the number 7 or not. Continue this process up to the result is multiple of 7 or 0.

Some Examples on divisibility rule of 7:

Example No.1:

Is 5689712 is divisible by the 7 or not?

Solution:

First double unit digit and subtract from remaining number.

Unit digit is 2, so its double is 4. Other than unit digit, remaining number is 568971.

Now subtract 4 from 568971, we get 568967. Now check 568967 is divisible by 7 or not. If you feel that, it is difficult to find it. No problem, again repeat the process.

Unit digit in 568967 is 7. Double of 7 is 14. Subtract 14 from 56896, we get 56882.

Unit digit in 56882 is 2. Double of 2 is 4. Subtract 4 from 5688, we get 5684.

In 5684, unit digit is 4. Double of 4 is 8. Subtract 8 from 568, we get 560.

In 560, 0 is the unit place. Double of 0 is 0. Subtract 0 from 56, we get 56.

Now it is clear that 56 is divisible by 7. So the above given number 5689712 is divisible by 7.

Example No.2:

Is the number 6273 is divisible by the 7?

Solution:

In 6273, unit digit is 3. Double of 3 is 6. So subtract 6 from 627, we get 621.

1 is the unit digit in 621. Double of 1 is 1. Subtract the number 1 from 62, we get the result as 61.

We know that, 61 is not divisible by the number 7, so, the give number 6273 is not divisible by the number 7.

Example No.3:

Is the number 504 is divisible by the 7?

Solution:

Unit digit double is 8. Subtract 8 from 50, we get 42. As 42 is divisible by 7, so 504 is divisible by 7.

Example No.4:

Is the number 1735 is divisible by the 7?

Solution:

173-(2×5)= 173-10= 163.

16 -(2×3)= 16-6 = 10.

We know that, 10 is not divisible by the number 7. So, the given number 1735 is not divisible by the number 7.

Example No.5:

Is the number 82149 is divisible by the 7?

Solution:

8214 – (2×9) = 8214 – 18 = 8196.

819 – (2×6) = 819 – 12 = 807.

80 – (2×7) = 80 – 14 = 66.

We know that, 66 is not divisible by the number 7. So, the given number 82149 is not divisible by the number 7.

Example No.6:

Is the 99257 is divisible by the 7?

Solution:

9925 – (2×7) = 9925 – 14 = 9911.

991 – (2×1) = 991 – 2 = 989.

98 –(2×9) = 98 – 18 = 80.

We know that, 80 is not divisible by the number 7. So, the given number 99257 is not divisible by the number 7.

I hope you have understood divisibility rule of 7 and examples based on it.

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