Divisibility Rule of 31
2026-02-28 23:27 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 31.

What is the Divisibility Rule of 31?

The divisibility rule for 31 is a method by which we can find out if a number is divisible by 31 or not without using the division method. Check whether 372 is divisible by 31 with the divisibility rule.

Step 1: Multiply the last digit of the number by 3, here in 372, 2 is the last digit. Multiply it by 3. 2 × 3 = 6.

Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 37 - 6 = 31.

Step 3: As it is shown that 31 is a multiple of 31, therefore, the number is divisible by 31. If the result from step 2 isn't a multiple of 31, then the number isn't divisible by 31.

Tips and Tricks for Divisibility Rule of 31

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 31.

  • Know the multiples of 31:  Memorize the multiples of 31 (31, 62, 93, 124, 155, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 31, then the number is divisible by 31.
     
  • Use the negative numbers:  If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
     
  • Repeat the process for large numbers:  Students should keep repeating the divisibility process until they reach a small number that is divisible by 31.  

    For example: Check if 5893 is divisible by 31 using the divisibility test.  

    Multiply the last digit by 3, i.e., 3 × 3 = 9.  Subtract the remaining digits excluding the last digit by 9, 589 - 9 = 580.  

    Still, 580 is a large number, hence we will repeat the process again and multiply the last digit by 3, 0 × 3 = 0.  

    Now subtracting 0 from the remaining numbers excluding the last digit, 58 - 0 = 58.  58 is not a multiple of 31, so 5893 is not divisible by 31.

  • Use the division method to verify:  Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 31

The divisibility rule of 31 helps us to quickly check if the given number is divisible by 31, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.

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Problem 1

Is 341 divisible by 31?

Okay, lets begin

Yes, 341 is divisible by 31.

Explanation

To check if 341 is divisible by 31:


1) Multiply the last digit by 3, 1 × 3 = 3.


2) Subtract the result from the remaining digits, 34 - 3 = 31.


3) Since 31 is a multiple of 31, 341 is divisible by 31.

Well explained 👍

Problem 2

Check the divisibility rule of 31 for 620.

Okay, lets begin

No, 620 is not divisible by 31

Explanation

For checking the divisibility of 620:


1) Multiply the last digit by 3, 0 × 3 = 0.


2) Subtract the result from the remaining digits, 62 - 0 = 62.


3) Since 62 is not a multiple of 31, 620 is not divisible by 31.

Well explained 👍

Problem 3

Is -155 divisible by 31?

Okay, lets begin

No, -155 is not divisible by 31.

Explanation

To check if -155 is divisible by 31:


1) Ignore the negative sign and multiply the last digit by 3, 5 × 3 = 15.


2) Subtract the result from the remaining digits, 15 - 15 = 0.


3) Since 0 is not a multiple of 31, -155 is not divisible by 31.

Well explained 👍

Problem 4

Can 1240 be divisible by 31 following the divisibility rule?

Okay, lets begin

Yes, 1240 is divisible by 31.

Explanation

To check if 1240 is divisible by 31:


1) Multiply the last digit by 3, 0 × 3 = 0.


2) Subtract the result from the remaining digits, 124 - 0 = 124.


3) Since 124 is a multiple of 31 (31 × 4 = 124), 1240 is divisible by 31.

Well explained 👍

Problem 5

Check the divisibility rule of 31 for 961.

Okay, lets begin

Yes, 961 is divisible by 31. 

Explanation

To check the divisibility rule of 31 for 961:


1) Multiply the last digit by 3, 1 × 3 = 3.


2) Subtract the result from the remaining digits, 96 - 3 = 93.


3) Since 93 is a multiple of 31 (31 × 3 = 93), 961 is divisible by 31.

Well explained 👍

FAQs on Divisibility Rule of 31

1.What is the divisibility rule for 31?

 The divisibility rule for 31 is multiplying the last digit by 3, then subtracting the result from the remaining digits excluding the last digit, and then checking if the result is a multiple of 31.

2.How many numbers are there between 1 and 100 that are divisible by 31?

 There are 3 numbers that can be divided by 31 between 1 and 100. The numbers are 31, 62, and 93.

3.Is 62 divisible by 31?

Yes, because 62 is a multiple of 31 (31 × 2 = 62).

4.What if I get 0 after subtracting?

If you get 0 after subtracting, it is considered as the number is divisible by 31.

5.Does the divisibility rule of 31 apply to all the integers?

Yes, the divisibility rule of 31 applies to all the integers.

Important Glossaries for Divisibility Rule of 31

  • Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 31 if the process described leads to a multiple of 31.
     
  • Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 31 are 31, 62, 93, 124, etc.
     
  • Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
     
  • Subtraction: Subtraction is the process of finding out the difference between two numbers by reducing one number from another.
     
  • Verification: The process of using division to confirm the result of a divisibility test.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.