Divisibility Rule of 45
2026-02-28 13:08 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 45.

What is the Divisibility Rule of 45?

The divisibility rule for 45 is a method by which we can find out if a number is divisible by 45 or not without using the division method. Check whether 180 is divisible by 45 with the divisibility rule.
 

Step 1: Ensure the number is divisible by both 5 and 9. A number is divisible by 5 if it ends in 0 or 5, and divisible by 9 if the sum of its digits is a multiple of 9.

Step 2: Check divisibility by 5. Here, 180 ends in 0, so it is divisible by 5.

Step 3: Check divisibility by 9. Sum the digits of 180: 1 + 8 + 0 = 9. Since 9 is a multiple of 9, 180 is divisible by 9.

Step 4: Since 180 is divisible by both 5 and 9, it is divisible by 45.

Tips and Tricks for Divisibility Rule of 45

Learning divisibility rules can help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 45.

  • Know the multiples of 45: Memorize the multiples of 45 (45, 90, 135, 180…etc.) to quickly check divisibility. If a number is divisible by both 5 and 9, then it is divisible by 45.
     
  • Use the sum of digits: For divisibility by 9, sum the digits and check if the result is a multiple of 9.
     
  • Check the last digit: For divisibility by 5, the last digit should be 0 or 5.
     
  • Repeat the process for large numbers: For larger numbers, break down the number into smaller parts to check divisibility by 5 and 9 separately.
     
  • 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 45

The divisibility rule of 45 helps us quickly check if a given number is divisible by 45, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you to avoid them.

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Problem 1

Is 360 divisible by 45?

Okay, lets begin

Yes, 360 is divisible by 45.
 

Explanation

To determine if a number is divisible by 45, it must be divisible by both 5 and 9. 

1) Check divisibility by 5: The last digit of 360 is 0, which is divisible by 5.

2) Check divisibility by 9: Sum the digits of 360 (3 + 6 + 0 = 9). The sum is 9, which is divisible by 9.

Therefore, 360 is divisible by 45.

Well explained 👍

Problem 2

Can 540 be divided by 45 without a remainder?

Okay, lets begin

Yes, 540 is divisible by 45.

Explanation

A number is divisible by 45 if it is divisible by both 5 and 9.

1) Check divisibility by 5: The last digit of 540 is 0, which is divisible by 5.

2) Check divisibility by 9: Sum the digits of 540 (5 + 4 + 0 = 9). The sum is 9, which is divisible by 9.
Thus, 540 is divisible by 45.

Well explained 👍

Problem 3

Is 225 divisible by 45?

Okay, lets begin

No, 225 is not divisible by 45.

Explanation

To check divisibility by 45, the number must be divisible by both 5 and 9.

1) Check divisibility by 5: The last digit of 225 is 5, which is divisible by 5.

2) Check divisibility by 9: Sum the digits of 225 (2 + 2 + 5 = 9). The sum is 9, which is divisible by 9.

Although 225 is divisible by both 5 and 9, when divided by 45, it does not leave a whole number (225 ÷ 45 = 5).

Therefore, 225 is not divisible by 45.

Well explained 👍

Problem 4

Verify if 945 is divisible by 45.

Okay, lets begin

Yes, 945 is divisible by 45.

Explanation

A number is divisible by 45 if it is divisible by both 5 and 9.

1) Check divisibility by 5: The last digit of 945 is 5, which is divisible by 5.

2) Check divisibility by 9: Sum the digits of 945 (9 + 4 + 5 = 18). The sum is 18, which is divisible by 9 (9 x 2 = 18).

Therefore, 945 is divisible by 45.

Well explained 👍

Problem 5

Determine if 1,080 can be divided by 45 without a remainder.

Okay, lets begin

Yes, 1,080 is divisible by 45.

Explanation

A number is divisible by 45 if it is divisible by both 5 and 9.

1) Check divisibility by 5: The last digit of 1,080 is 0, which is divisible by 5.

2) Check divisibility by 9: Sum the digits of 1,080 (1 + 0 + 8 + 0 = 9). The sum is 9, which is divisible by 9.

Therefore, 1,080 is divisible by 45.

Well explained 👍

FAQs on Divisibility Rule of 45

1.What is the divisibility rule for 45?

The divisibility rule for 45 is that a number must be divisible by both 5 and 9. Check if it ends in 0 or 5 (for 5) and if the sum of its digits is a multiple of 9 (for 9).
 

2.How many numbers are there between 1 and 200 that are divisible by 45?

There are four numbers that can be divided by 45 between 1 and 200. The numbers are - 45, 90, 135, and 180.

3.Is 225 divisible by 45?

Yes, because 225 is divisible by both 5 (it ends in 5) and 9 (2 + 2 + 5 = 9, which is a multiple of 9).

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

If the sum of the digits is 0, it indicates that the number is divisible by 9, provided it also meets other conditions for divisibility by 45.

5.Does the divisibility rule of 45 apply to all integers?

Yes, the divisibility rule of 45 applies to all integers.

Important Glossaries for Divisibility Rule of 45

  • Divisibility rule: A set of guidelines used to determine whether a number is divisible by another number without performing the full division.
     
  • Multiples: The results of multiplying a number by an integer. For example, multiples of 45 are 45, 90, 135, 180, etc.
     
  • Integers: Numbers that include all whole numbers, negative numbers, and zero.
     
  • Sum of digits: The result of adding all the digits of a number together, used to check divisibility by 9.
     
  • Divisibility by 5: A rule stating a number is divisible by 5 if its last digit is 0 or 5.
     

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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.