# Divisibility Rule of 7, 11, and 13 – with Examples

Hello friends, in this tutorial you will learn about the divisibility rule of 7, the divisibility rule of 11, and the divisibility rule of 13. These rules are explained with the help of example questions.

We have also provided some practice questions at the end of the post so that you can practice and memorize these rules easily. You can find more divisibility rules here.

So, let’s get started.

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## Divisibility rule of 7

The divisibility rule of 7 is an important rule as the number 7 belongs to the digits (0-9) and it is recommended to memorize the divisibility rule from 2 to 9 at least for quick calculations and problem-solving in school or competitive exams.

There are two different rules depending upon the type of number (small or large). You can check both rules here:

### Divisibility rule of 7 for small numbers (three or four digits)

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

Follow the below steps to test the divisibility of numbers having 3-4 digits:

1. Subtract the twice of digit at the unit place from the remaining part
2. If the result is 0 or a multiple of 7, the number is divisible by 7.

Example,

For a number 693, Twice the digit at one’s place, 3×2 = 6, and the difference, 69-6 = 63, which is a multiple of 7. Hence, 693 is divisible by 7.

Also, for a number 407, twice the unit digit, 7×2 = 14, and the difference, 40-14 = 26, which is not a multiple of 7. Hence, 407 is not divisible by 7.

The above method allows you to quickly test for the divisibility by 7. But, for the large numbers, it may not be of that much help.

For large numbers (More than 5 digits), follow another rule to test divisibility by 7.

### Divisibility rule of 7 for large numbers

To test the divisibility of a large number having 5 or more digits, follow the below steps.

1. Divide the number into groups of three digits starting from the right
2. Find the difference between the sum of numbers in odd and even places.
3. If the difference is either 0 or a multiple of 7, the number is divisible by 7

Example,

Let’s follow the divisibility rule of 7 for the number 5295493

• According to the first steps, 5295493 can be divided into three groups from the right as 5 / 295 / 493.
• Now, the difference of the sum of numbers in odd and even places, (5+493) – 295 = 203 which when divided by 7 gives 29.

Hence, the number 5295493 is divisible by 7.

You may want to check: All the maths formulas for Class 9 and Class 10

## Divisibility rule of 11

The divisibility rule of 11 states, “If the difference between the sum of digits at the odd place and the sum of digits at even place is either 0 or multiple of 11, then the number is divisible by 11”.

Examples,

For a number 6586547, test the divisibility by following the below steps:

• Find the sum of digits at the odd place (i.e., 6+8+5+7= 26) and the sum of digits at an even place (i.e., 5+6+4 = 15).
• Difference between both sums, 26 – 15 = 11, which is a multiple of 11. Hence, the number is divisible by 11.

Similarly, for a number 659826, the difference between the sum of odd place digits and even place digits is, (6+8+5) – (2+9+6) = 2, hence 659826 is not divisible by 11.

## Divisibility rule of 13

The divisibility rule of 13 is similar to that of the divisibility rule of 7 for large numbers. Follow the below steps to test for the divisibility by 13.

1. Divide the number into groups of three digits starting from the right
2. Find the difference between the sum of numbers in odd and even places.
3. If the difference is either 0 or a multiple of 13, the number is divisible by 13

For example, let’s check the divisibility of 1039974 by 13.

Dividing the number into groups of three digits gives 1 / 039 / 974. The difference between the sum of numbers in odd and even places gives, (1+974) – 039 = 936 which is divisible by 13.

Hence, 1039974 is also divisible by 13.

You can test the divisibility rule of 13 by trying out more examples we have shared below.

## Practice Questions

Q. Use the divisibility rule of 13 and divisibility rule of 11 to test the divisibility for the following numbers:

• 1412268
• 45699210
• 2924207
• 12471030

Q. What is the lowest number that is divisible by both 11 and 13?
Q. What is the lowest number that is divisibility by 7, 11, and 13?
Q. Write three numbers that are divisible by every number between 2 to 13.

## More Divisibility rules

That was all about the divisibility rule of 7, 11, and 13. If you have any suggestions or feedback, please do not hesitate to share them with us. In the meantime, practice well and memorize all the divisibility rules from 2 to 20.

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