Divisibility Rule of 7

In Mathematics, the divisibility rule or divisibility test is a method to determine whether the given number is divisible by a fixed divisor, without performing the division operation. This method generally uses the digits to find the given number is divided by a divisor. We can say, if a number is perfectly divisible by the other number, the remainder should be zero, and the quotient should be a whole number. We have divisibility rules for 1, 2, 3, 4, 5, 6, 7,8, 9, 10, 11, 12, 13, and so on. In this article, we are going to discuss the “Divisibility Rule of 7” with many solved examples.

Table of Contents:

What is the Divisibility Rule of 7?

The divisibility rule of 7 states that, if a number is divisible by 7, then “the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0”.

For example, 798 is divisible by 7.

Explanation:

The unit digit of 798 is 8.

If the unit digit is doubled, we get 16 (i.e., 8 x 2 = 16)

The remaining part of the given number is 79.

Now, take the difference between 79 and 16.

= 79-16

=63

Here, the difference value obtained is 63, which is a multiple of 7. (i.e., 9 x 7 = 63)

Thus, the given number 798 is divisible by 7.

Also, read: Divisibility Rules for 13.

Divisibility Rule of 7 Examples

The following solved examples help you to understand the divisibility rule of 7.

Example 1:

Which of the following numbers is divisible by 7?

  1. 171
  2. 119
  3. 107
  4. 383

Solution:

A correct answer is option (b) 119

Explanation:

(a) 171

Step 1: Double the unit digit = 1 x 2 = 2

Step 2: Difference = 17 – 2 = 15

15 is not a multiple of 7, and hence 171 is not divisible by 7.

(b) 119

Step 1: Double the unit digit = 9 x 2 = 18

Step 2: Difference = 11 – 18 = -7, which is a multiple of 7

Hence, 119 is divisible by 7.

(c) 107

Step 1: Double the unit digit = 7 x 2 = 14

Step 2: Difference = 10 – 14 = -4, which is not a multiple of 7.

Hence, 107 is not divisible by 7.

(d) 383

Step 1: Double the unit digit = 3 x 2 = 6

Step 2: Difference = 38 – 6 = 32, which is not a multiple of 7.

Thus, 383 is not divisible by 7.

Example 2:

Check whether a number 449 is divisible by 7.

Solution:

Given number = 449.

To check whether a number 449 is divisible by 7, follow the below steps.

Step 1: Double the unit digit = 9 x 2 = 18

Step 2: Take the difference between the remaining part of the given number and the result obtained from step 1. (i.e., 18)

= 44 – 18

= 26, which is not a multiple of 7.

Hence, the given number 449 is not divisible by 7.

Practice Problems

Check the following numbers are divisible by 7, using the divisibility rule of 7.

  1. 595
  2. 133
  3. 233
  4. 305
  5. 672

Frequently Asked Questions on Divisibility Rule of 7

What is the divisibility rule of 7?

The divisibility rule of 7 helps to find the given number is divisible by 7, without performing division operation. The divisibility rule of 7 states that, if a number is divisible 7, then the difference between twice the unit digit of the given number and the remaining part of the given number should be equal to 0, or the multiples of 7.

How many numbers are there between 1 and 100 are divisible by 7?

There are 14 numbers between 1 and 100, which are exactly divisible by 7. They are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

Is 28 divisible by 7?

Yes, 28 is divisible by 7. Because, 28 is a multiple of 7. (i.e, 4 x 7 = 28).

Is 105 divisible by 7?

Yes, 105 is divisible by 7.

Explanation:

Double the unit digit = 5 x 2 = 10

Remaining part of the given number = 10

Thus, the difference between twice the unit digit and the remaining part of the given number is 0 (i.e.) 10-10 = 0.

Is 905 divisible by 7?

No, 905 is not divisible by 7.

Explanation:

Double the unit digit = 5 x 2 = 10

Remaining part of the given number = 90

Thus, the difference between twice the unit digit and the remaining part of the given number is 80, which is not a multiple of 7 (i.e.) 90-10 = 80.

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