365 LearnersLast updated on May 26th, 2025
Divisibility Rule of 36
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 36.
What is the Divisibility Rule of 36?
The divisibility rule for 36 is a method by which we can find out if a number is divisible by 36 or not without using the division method. Check whether 216 is divisible by 36 with the divisibility rule.
Step 1: Check if the number is divisible by both 4 and 9, as 36 is the product of these two numbers.
Step 2: To check divisibility by 4, look at the last two digits. If the last two digits form a number that is divisible by 4, then the number is divisible by 4. Here, 16 is divisible by 4.
Step 3: To check divisibility by 9, add all the digits of the number. If the sum is divisible by 9, then the number is divisible by 9. For 216, 2+1+6=9, which is divisible by 9.
Step 4: Since 216 is divisible by both 4 and 9, it is divisible by 36.
Tips and Tricks for Divisibility Rule of 36
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 36.
- Know the multiples of 36: Memorize the multiples of 36 (36, 72, 108, 144, etc.) to quickly check divisibility. If the result confirms the number is a multiple of both 4 and 9, then it is divisible by 36.
- Use smaller divisibility rules: Since 36 is composed of 4 and 9, use these smaller rules for easier calculations.
- Repeat the process for large numbers: For larger numbers, apply the divisibility tests for 4 and 9 separately. For example, check if 1296 is divisible by 36. The last two digits, 96, are divisible by 4, and 1+2+9+6=18, which is divisible by 9. Thus, 1296 is divisible by 36.
- Use the division method to verify: Students can use the division method 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 36
The divisibility rule of 36 helps us quickly check if a given number is divisible by 36, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking both divisibility rules.
Students should check divisibility by both 4 and 9 to ensure the number is divisible by 36.
Divisibility Rule of 36 Examples
Problem 1
Is the total number of seats in a theater, 720, divisible by 36?
Yes, 720 is divisible by 36.
Explanation
To check if 720 is divisible by 36, we need to ensure it is divisible by both 4 and 9.
1) Check divisibility by 4: The last two digits are 20, which is not divisible by 4. Therefore, 720 is not divisible by 36.
Problem 2
A company produced 1,296 widgets this month. Can this number be evenly divided into boxes that hold 36 widgets each?
Yes, 1,296 is divisible by 36.
Explanation
To determine if 1,296 is divisible by 36, ensure it's divisible by both 4 and 9.
1) Check divisibility by 4: The last two digits are 96. Since 96 ÷ 4 = 24, it is divisible by 4.
2) Check divisibility by 9: The sum of the digits is 1 + 2 + 9 + 6 = 18, and 18 ÷ 9 = 2, so it's divisible by 9.
Since 1,296 is divisible by both 4 and 9, it is divisible by 36.
Problem 3
A library received 432 new books, which need to be arranged in sections containing 36 books. Is this possible without any leftovers?
Yes, 432 is divisible by 36.
Explanation
To check if 432 is divisible by 36, it must be divisible by both 4 and 9.
1) Check divisibility by 4: The last two digits are 32. Since 32 ÷ 4 = 8, it is divisible by 4.
2) Check divisibility by 9: The sum of the digits is 4 + 3 + 2 = 9, and 9 ÷ 9 = 1, so it's divisible by 9.
432 is divisible by both 4 and 9, confirming it is divisible by 36.
Problem 4
A batch of 575 cookies needs to be divided into boxes containing 36 cookies each. Can this be done without breaking cookies?
No, 575 is not divisible by 36.
Explanation
To check if 575 is divisible by 36, ensure it is divisible by both 4 and 9.
1) Check divisibility by 4: The last two digits are 75, which is not divisible by 4. Thus, 575 is not divisible by 36.
Problem 5
Is the number of pages in a book, 864, divisible by 36, such that each chapter can have an equal number of pages?
Yes, 864 is divisible by 36.
Explanation
To determine if 864 is divisible by 36, it must be divisible by both 4 and 9.
1) Check divisibility by 4: The last two digits are 64. Since 64 ÷ 4 = 16, it is divisible by 4.
2) Check divisibility by 9: The sum of the digits is 8 + 6 + 4 = 18, and 18 ÷ 9 = 2, so it's divisible by 9.
Since 864 is divisible by both 4 and 9, it is divisible by 36.
FAQs on Divisibility Rule of 36
1.What is the divisibility rule for 36?
2.How many numbers are there between 1 and 200 that are divisible by 36?
3.Is 144 divisible by 36?
4.What if I get 0 after checking for divisibility by 9?
5.Does the divisibility rule of 36 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 36?
7.What are some fun ways kids in India can practice Divisibility Rule of 36 with numbers?
8.What role do numbers and Divisibility Rule of 36 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 36 skills?
Important Glossaries for Divisibility Rule of 36
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number without performing division.
- Multiples: The results obtained after multiplying a number by an integer. For example, multiples of 36 are 36, 72, 108, etc.
- Integers: Whole numbers that include positive numbers, negative numbers, and zero.
- Sum of digits: Adding all the digits of a number to check for divisibility, especially for rules like divisibility by 9.
- Last two digits: The last two digits of a number, used to check divisibility by 4.
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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
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