180 LearnersLast updated on May 26th, 2025
Divisibility Rule of 90
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 90.
What is the Divisibility Rule of 90?
The divisibility rule for 90 is a method by which we can find out if a number is divisible by 90 or not without using the division method. To determine if a number is divisible by 90, it must be divisible by both 9 and 10.
Let's check whether 450 is divisible by 90 with the divisibility rule:
Step 1: Check divisibility by 10. A number is divisible by 10 if its last digit is 0. In 450, the last digit is 0, so it is divisible by 10.
Step 2: Check divisibility by 9. A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of the digits in 450 is 4 + 5 + 0 = 9, which is divisible by 9.
Step 3: Since 450 is divisible by both 10 and 9, it is divisible by 90.
Tips and Tricks for Divisibility Rule of 90
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 90.
- Know the multiples of 90: Memorize the multiples of 90 (90, 180, 270, 360, etc.) to quickly check divisibility. If both conditions for divisibility by 9 and 10 are met, the number is divisible by 90.
- Use the sum of digits for 9: Always calculate the sum of the digits of the number to check divisibility by 9. Ensure the result is a multiple of 9.
- Repeat for large numbers: If needed, repeat the process to simplify or verify calculations.
- 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 90
The divisibility rule of 90 helps us quickly check if a given number is divisible by 90, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which include checking for divisibility by both 9 and 10.
Divisibility Rule of 90 Examples
Problem 1
Is 540 divisible by 90?
Yes, 540 is divisible by 90.
Explanation
To check if 540 is divisible by 90, we use the rules for divisibility by 9 and 10.
1) For divisibility by 9, sum the digits: 5 + 4 + 0 = 9. Since 9 is divisible by 9, 540 is divisible by 9.
2) For divisibility by 10, check if the last digit is 0. Since the last digit is 0, 540 is divisible by 10.
Since 540 is divisible by both 9 and 10, it is divisible by 90.
Problem 2
Check if 720 is divisible by 90.
No, 720 is not divisible by 90.
Explanation
To determine if 720 is divisible by 90, we check divisibility by 9 and 10.
1) For divisibility by 9, sum the digits: 7 + 2 + 0 = 9. Since 9 is divisible by 9, 720 is divisible by 9.
2) For divisibility by 10, check if the last digit is 0. Since the last digit is 0, 720 is divisible by 10.
Despite being divisible by both 9 and 10, we need to check for exact division by 90. 720 ÷ 90 = 8, which is not an integer, indicating an error in reasoning. Please correct this: 720 ÷ 90 = 8, which is an integer, so 720 is indeed divisible by 90.
Problem 3
Is 450 divisible by 90?
No, 450 is not divisible by 90.
Explanation
To check if 450 is divisible by 90, we examine divisibility by 9 and 10.
1) For divisibility by 9, sum the digits: 4 + 5 + 0 = 9. Since 9 is divisible by 9, 450 is divisible by 9.
2) For divisibility by 10, check if the last digit is 0. Since the last digit is 0, 450 is divisible by 10.
However, 450 ÷ 90 = 5, resulting in an integer, indicating a correction is needed here. 450 is indeed divisible by 90.
Problem 4
Can 360 be divisible by 90 following the divisibility rule?
Yes, 360 is divisible by 90.
Explanation
To check if 360 is divisible by 90, we apply the divisibility rules for 9 and 10.
1) For divisibility by 9, sum the digits: 3 + 6 + 0 = 9. Since 9 is divisible by 9, 360 is divisible by 9.
2) For divisibility by 10, check if the last digit is 0. Since the last digit is 0, 360 is divisible by 10.
Since 360 is divisible by both 9 and 10, it is divisible by 90.
Problem 5
Check if 810 is divisible by 90.
Yes, 810 is divisible by 90.
Explanation
To determine if 810 is divisible by 90, we use the divisibility rules for 9 and 10.
1) For divisibility by 9, sum the digits: 8 + 1 + 0 = 9. Since 9 is divisible by 9, 810 is divisible by 9.
2) For divisibility by 10, check if the last digit is 0. Since the last digit is 0, 810 is divisible by 10.
Since 810 is divisible by both 9 and 10, it is divisible by 90.
FAQs on Divisibility Rule of 90
1.What is the divisibility rule for 90?
2.How many numbers are there between 1 and 500 that are divisible by 90?
3.Is 270 divisible by 90?
4.What if I get 0 for the sum of digits?
5.Does the divisibility rule of 90 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 90?
7.What are some fun ways kids in United States can practice Divisibility Rule of 90 with numbers?
8.What role do numbers and Divisibility Rule of 90 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 90 skills?
Important Glossaries for Divisibility Rule of 90
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number without direct division. For example, a number is divisible by 10 if it ends in 0.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 90 are 90, 180, 270, etc.
- Sum of digits: The total obtained by adding all the digits of a number. Used to determine divisibility by 9.
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
- Last digit check: The process of examining the last digit of a number to determine divisibility by 10.
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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.
