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What does the number 7 rule?

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”.

byjus.com - Divisibility Rule of 7 (Rules and Examples) | Divisibility Test for 7
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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?

171 119 107 383

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.

595 133 233 305 672

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Challenge 1 — Reverse the Golden Rule

The golden rule demands that we treat others the way we’d like to be treated. Sometimes, though, we blame or derogate ourselves for even the slightest failure—even if we’d be compassionate and understanding towards someone else who failed the same way. This sort of toxic perfectionism creates anxiety and depression, and can make it harder to connect with others, too. Today try reversing the golden rule—treating yourself the way you’d treat other people. Think back to a recent failure, or time you disappointed yourself. Now imagine that a close friend or family member failed in exactly the same way. What would you say to them, how would you feel about them, and how would you want them to feel? Finally, turn that same lens back on yourself—trying to give yourself the same grace and compassion to yourself that you’d give to a someone you love.

Reflect on this experience. Were you initially harder on yourself than you would be towards someone close to you? Did reversing the golden rule allow you more self-compassion? How could you apply this strategy during hard times in the future?

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