330 LearnersLast updated on May 26th, 2025
Divisibility Rule of 33
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 33.
What is the Divisibility Rule of 33?
The divisibility rule for 33 is a method by which we can find out if a number is divisible by 33 or not without using the division method. Check whether 396 is divisible by 33 with the divisibility rule.
Step 1: Check if the number is divisible by both 3 and 11. First, we apply the divisibility rule for 3: Add the digits of the number. For 396, 3 + 9 + 6 = 18. Since 18 is divisible by 3, the number passes the first part of the test.
Step 2: Now, apply the divisibility rule for 11: Find the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions. For 396, (3 + 6) - 9 = 0. Since 0 is divisible by 11, the number passes the second part of the test.
Step 3: As 396 passes both tests, it is divisible by 33.
Tips and Tricks for Divisibility Rule of 33
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 33.
- Know the multiples of 33: Memorize the multiples of 33 (33, 66, 99, 132, 165, etc.) to quickly check divisibility. If the result from the operations is a multiple of 33, then the number is divisible by 33.
- Use the divisibility rules for 3 and 11: Ensure the number is divisible by both 3 and 11 to conclude that it is divisible by 33.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by both 3 and 11. For example, check if 5943 is divisible by 33 using the divisibility test. Apply the rule for 3: 5 + 9 + 4 + 3 = 21, which is divisible by 3. Then, for 11: (5 + 4) - (9 + 3) = -3, which is not divisible by 11. So, 5943 is not divisible by 33.
- 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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 33
The divisibility rule of 33 helps us to quickly check if the given number is divisible by 33, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to avoid them.
Mistake 1
Not checking divisibility by both 3 and 11.
Students should ensure that a number is divisible by both 3 and 11 to conclude divisibility by 33.
Divisibility Rule of 33 Examples
Problem 1
Can 396 be divided by 33 without a remainder?
Yes, 396 is divisible by 33.
Explanation
To determine if 396 is divisible by 33, you can use the divisibility rules for both 3 and 11, since 33 is the product of these two numbers.
1) Check divisibility by 3: Add the digits, 3 + 9 + 6 = 18, which is divisible by 3.
2) Check divisibility by 11: Calculate the alternating sum of the digits, 3 - 9 + 6 = 0, which is divisible by 11.
Since 396 meets both conditions, it is divisible by 33.
Problem 2
Is 561 divisible by 33?
No, 561 is not divisible by 33.
Explanation
To check divisibility by 33, use divisibility rules for 3 and 11.
1) Check divisibility by 3: Add the digits, 5 + 6 + 1 = 12, which is divisible by 3.
2) Check divisibility by 11: Calculate the alternating sum, 5 - 6 + 1 = 0, which is divisible by 11.
Though 561 satisfies both divisibility rules, there was an error in the explanation, the number 561 is indeed divisible by 33.
Problem 3
Verify if 726 is divisible by 33.
Yes, 726 is divisible by 33.
Explanation
Use the divisibility rules for 3 and 11.
1) Check divisibility by 3: Add the digits, 7 + 2 + 6 = 15, which is divisible by 3.
2) Check divisibility by 11: Calculate the alternating sum, 7 - 2 + 6 = 11, which is divisible by 11.
Since both conditions are met, 726 is divisible by 33.
Problem 4
Is 880 divisible by 33?
No, 880 is not divisible by 33.
Explanation
To determine divisibility by 33, check divisibility by 3 and 11.
1) Check divisibility by 3: Add the digits, 8 + 8 + 0 = 16, which is not divisible by 3.
Since 880 is not divisible by 3, it cannot be divisible by 33.
Problem 5
Can 1089 be divided by 33 without a remainder?
Yes, 1089 is divisible by 33.
Explanation
Check divisibility by 3 and 11.
1) Check divisibility by 3: Add the digits, 1 + 0 + 8 + 9 = 18, which is divisible by 3.
2) Check divisibility by 11: Calculate the alternating sum, 1 - 0 + 8 - 9 = 0, which is divisible by 11.
Since both conditions are satisfied, 1089 is divisible by 33.
FAQs on Divisibility Rule of 33
1.What is the divisibility rule for 33?
2.How many numbers are there between 1 and 100 that are divisible by 33?
3.Is 132 divisible by 33?
4.What if I get 0 after applying the rules for 11?
5.Does the divisibility rule of 33 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 33?
7.What are some fun ways kids in India can practice Divisibility Rule of 33 with numbers?
8.What role do numbers and Divisibility Rule of 33 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 33 skills?
Important Glossary for Divisibility Rule of 33
- Divisibility rule: A set of rules used to determine if a number is divisible by another number without direct division.
- Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 33 are 33, 66, 99, 132, etc.
- Sum of digits: The result of adding all the digits in a number, used in checking divisibility by 3.
- Difference of sums: For divisibility by 11, the difference between the sum of digits in odd and even positions.
- Integer: A whole number that can be positive, negative, or zero.
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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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