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What is the rule number 7?

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.

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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Which god is responsible for wealth?

Lakshmi, also spelled Lakṣmī, also called Shri, Hindu goddess of wealth and good fortune.

britannica.com - Lakshmi | Hindu deity - Encyclopedia Britannica

Lakshmi, also spelled Lakṣmī, also called Shri, Hindu goddess of wealth and good fortune. The wife of Vishnu, she is said to have taken different forms in order to be with him in each of his incarnations. Thus, when he was the dwarf Vamana, she appeared from a lotus and was known as Padma, or Kamala, both of which mean “Lotus”; when he was the ax-wielding Parashurama, the destroyer of the warrior class, she was his wife Dharani; when he was King Rama, she was his queen Sita. In the most widely received account of Lakshmi’s birth, she rose from the churning of the ocean of milk (an important event in Hinduism), seated on a lotus and holding another blossom in her hand. Controversy arose between the gods and demons over possession of her. Lakshmi is often represented in sculpture seated on a lotus, full-breasted, broad-hipped, beneficently smiling, and sometimes being lustrated by a pair of elephants pouring water over her. Her vehicle is the white owl. She continues to be worshipped by modern Hindus, particularly in the home (every Friday) and on regular festival days throughout the year. She is greatly revered in Jainism.

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