Divisibility Rule of 108
2026-02-28 11:36 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 108.

What is the Divisibility Rule of 108?

The divisibility rule for 108 is a method by which we can find out if a number is divisible by 108 or not without using the division method. Check whether 324 is divisible by 108 with the divisibility rule.

Step 1: Check if the number is divisible by 4. The last two digits of 324 are 24, and since 24 is divisible by 4, we move to the next step.


Step 2: Check if the number is divisible by 9. Add the digits of 324: 3 + 2 + 4 = 9. Since 9 is divisible by 9, 324 is divisible by 108.
 

Tips and Tricks for Divisibility Rule of 108

Learn the divisibility rule to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 108.
 

  • Know the multiples of 108: Memorize the multiples of 108 (108, 216, 324, 432, etc.) to quickly check the divisibility. If a number matches these multiples, it is divisible by 108.
     
  • Use divisibility rules for smaller factors: Since 108 is made up of the factors 4 and 9, ensure a number is divisible by these smaller factors to confirm divisibility by 108.
     
  • Repeat the process for large numbers: Students should keep repeating the divisibility process for both 4 and 9 until they reach a conclusion about the number's divisibility by 108.
     
  • 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 verify and also learn.
     

Common Mistakes and How to Avoid Them in Divisibility Rule of 108

The divisibility rule of 108 helps us to quickly check if the given number is divisible by 108, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you understand.

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Problem 1

A charity event wants to distribute 216 raffle tickets evenly among 2 teams. Is it possible using the divisibility rule of 108?

Okay, lets begin

Yes, 216 is divisible by 108.

Explanation

To check divisibility by 108, verify divisibility by 2, 3, and 4.


1) Divisibility by 2: The last digit is 6, which is even.


2) Divisibility by 3: Sum of the digits (2 + 1 + 6 = 9) is divisible by 3.


3) Divisibility by 4: The last two digits, 16, are divisible by 4.


Since 216 satisfies divisibility by 2, 3, and 4, it is divisible by 108.

Well explained 👍

Problem 2

A rectangular garden has a perimeter of 432 meters. Can the length of the garden be 108 meters, using the divisibility rule of 108?

Okay, lets begin

Yes, 432 is divisible by 108.

Explanation

Check divisibility by 2, 3, and 4.


1) Divisibility by 2: The last digit is 2, which is even.


2) Divisibility by 3: Sum of the digits (4 + 3 + 2 = 9) is divisible by 3.


3) Divisibility by 4: The last two digits, 32, are divisible by 4.


Since 432 meets all criteria, it is divisible by 108.

Well explained 👍

Problem 3

A box contains 648 chocolates, and you want to pack them into smaller boxes, each holding 108 chocolates. Is this possible using the divisibility rule of 108?

Okay, lets begin

Yes, 648 is divisible by 108.

Explanation

Verify divisibility by 2, 3, and 4.


1) Divisibility by 2: The last digit is 8, an even number.


2) Divisibility by 3: Sum of the digits (6 + 4 + 8 = 18) is divisible by 3.


3) Divisibility by 4: The last two digits, 48, are divisible by 4.


Thus, 648 is divisible by 108.

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Well explained 👍

Problem 4

A library has 324 books to arrange in stacks of 108. Can this be done using the divisibility rule of 108?

Okay, lets begin

Yes, 324 is divisible by 108.
 

Explanation

Check divisibility by 2, 3, and 4.


1) Divisibility by 2: The last digit is 4, even.


2) Divisibility by 3: Sum of the digits (3 + 2 + 4 = 9) is divisible by 3.


3) Divisibility by 4: The last two digits, 24, are divisible by 4.


Therefore, 324 is divisible by 108.

Well explained 👍

Problem 5

A festival organizer has 432 flags to distribute evenly among 4 locations. Is it possible using the divisibility rule of 108?

Okay, lets begin

Yes, 432 is divisible by 108.

Explanation

Verify divisibility by 2, 3, and 4.


1) Divisibility by 2: The last digit is 2, which is even.


2) Divisibility by 3: Sum of the digits (4 + 3 + 2 = 9) is divisible by 3.


3) Divisibility by 4: The last two digits, 32, are divisible by 4.


Since all conditions are satisfied, 432 is divisible by 108.

Well explained 👍

FAQs on Divisibility Rule of 108

1.What is the divisibility rule for 108?

The divisibility rule for 108 is checking if a number is divisible by both 4 and 9. If it is divisible by both, then it is divisible by 108.

2.How many numbers are there between 1 and 1000 that are divisible by 108?

There are 9 numbers that can be divided by 108 between 1 and 1000. The numbers are 108, 216, 324, 432, 540, 648, 756, 864, and 972.

3.Is 432 divisible by 108?

Yes, because 432 is a multiple of 108 (108 × 4 = 432).
 

4.What if a number is divisible by 4 but not by 9?

The number is not divisible by 108 if it does not meet divisibility conditions for both 4 and 9.
 

5.Does the divisibility rule of 108 apply to all integers?

Yes, the divisibility rule of 108 applies to all integers.

Important Glossaries for Divisibility Rule of 108

  • 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 108 if it is divisible by both 4 and 9.
     
  • Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 108 are 108, 216, 324, 432, etc.
     
  • Factors: Factors are numbers you can multiply together to get another number. 108 has factors like 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
     
  • Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
     
  • Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
     

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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.