Divisibility Rule of 18
2026-02-28 14:07 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 18.

What is the Divisibility Rule of 18?

The divisibility rule for 18 is a method by which we can find out if a number is divisible by 18 or not without using the division method. A number is divisible by 18 if it is divisible by both 2 and 9.

Check whether 234 is divisible by 18 with the divisibility rule.

Step 1: Check divisibility by 2. A number is divisible by 2 if its last digit is even. In 234, 4 is the last digit, which is even, so 234 is divisible by 2.

Step 2: Check divisibility by 9. A number is divisible by 9 if the sum of its digits is a multiple of 9. Add the digits of 234: 2 + 3 + 4 = 9. Since 9 is a multiple of 9, 234 is divisible by 9.

Step 3: Since 234 is divisible by both 2 and 9, it is divisible by 18.

Tips and Tricks for Divisibility Rule of 18

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 18.

  • Know the multiples of 18: Memorize the multiples of 18 (18, 36, 54, 72, 90, etc.) to quickly check divisibility. If the result from the checks is a multiple of 18, then the number is divisible by 18.
  • Use the sum of digits: If checking for 9, always remember to sum the digits and see if they form a multiple of 9.
  • Repeat the process for large numbers: Students should keep repeating the divisibility process for both 2 and 9 until they reach a definitive conclusion.
  • Use the division method to verify: Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 18

The divisibility rule of 18 helps us to quickly check if the given number is divisible by 18, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.

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Problem 1

Is 324 divisible by 18?

Okay, lets begin

Yes, 324 is divisible by 18.

Explanation

To check if 324 is divisible by 18, we need to verify divisibility by both 2 and 9.

1) Check divisibility by 2: The last digit is 4, which is even, so 324 is divisible by 2.


2) Check divisibility by 9: Add the digits 3 + 2 + 4 = 9, which is divisible by 9.


Since 324 is divisible by both 2 and 9, it is divisible by 18.

Well explained 👍

Problem 2

Check the divisibility rule of 18 for 612.

Okay, lets begin

Yes, 612 is divisible by 18.

Explanation

To determine divisibility by 18, we check divisibility by 2 and 9.

1) Check divisibility by 2: The last digit is 2, which is even, so 612 is divisible by 2.


2) Check divisibility by 9: Sum the digits 6 + 1 + 2 = 9, which is divisible by 9.


Since 612 is divisible by both 2 and 9, it is divisible by 18.

Well explained 👍

Problem 3

Is 275 divisible by 18?

Okay, lets begin

No, 275 is not divisible by 18.

Explanation

For divisibility by 18, the number must be divisible by both 2 and 9.

1) Check divisibility by 2: The last digit is 5, which is not even, so 275 is not divisible by 2.


2) Check divisibility by 9: Sum the digits 2 + 7 + 5 = 14, which is not divisible by 9.


Since 275 is not divisible by 2 and not divisible by 9, it is not divisible by 18.

Well explained 👍

Problem 4

Can 972 be divisible by 18 following the divisibility rule?

Okay, lets begin

Yes, 972 is divisible by 18.

Explanation

We check divisibility by both 2 and 9.

1) Check divisibility by 2: The last digit is 2, which is even, so 972 is divisible by 2.


2) Check divisibility by 9: Sum the digits 9 + 7 + 2 = 18, which is divisible by 9.


Since 972 is divisible by both 2 and 9, it is divisible by 18.

Well explained 👍

Problem 5

Check the divisibility rule of 18 for 450.

Okay, lets begin

No, 450 is not divisible by 18.

Explanation

We must check divisibility by 2 and 9.

1) Check divisibility by 2: The last digit is 0, which is even, so 450 is divisible by 2.


2) Check divisibility by 9: Sum the digits 4 + 5 + 0 = 9, which is divisible by 9.


Although 450 is divisible by 9, it must also be divisible by 2 and 9. Since it is divisible by both, my previous conclusion was incorrect. 450 is actually divisible by 18.

Well explained 👍

FAQs on Divisibility Rule of 18

1. What is the divisibility rule for 18?

A number is divisible by 18 if it is divisible by both 2 and 9.

2.How many numbers are there between 1 and 100 that are divisible by 18?

There are 5 numbers divisible by 18 between 1 and 100. The numbers are 18, 36, 54, 72, 90.

3.Is 54 divisible by 18?

Yes, because 54 is a multiple of 18 (18 × 3 = 54).

4.What if I get 0 after summing the digits for 9?

If the sum of the digits is 0, it is considered as the number is divisible by 9.

5.Does the divisibility rule of 18 apply to all integers?

Yes, the divisibility rule of 18 applies to all integers.

Important Glossaries for Divisibility Rule of 18

  • Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
  • Multiples: The results we get after multiplying a number by an integer. For example, multiples of 18 are 18, 36, 54, etc.
  • Integers: Numbers that include all whole numbers, negative numbers, and zero.
  • Sum of digits: The total obtained by adding all the digits of a number.
  • Even number: A number that is divisible by 2.

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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.