153 LearnersLast updated on May 26th, 2025
Divisibility Rule of 66
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 66.
What is the Divisibility Rule of 66?
The divisibility rule for 66 is a method by which we can find out if a number is divisible by 66 or not without using the division method. A number is divisible by 66 if it is divisible by both 2 and 3 and 11. This means:
1. The number must be even (divisible by 2).
2. The sum of the digits must be divisible by 3.
3. The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be a multiple of 11.
Check whether 1452 is divisible by 66 using the divisibility rule.
Step 1: Check divisibility by 2. Since 1452 ends in 2, it is divisible by 2.
Step 2: Check divisibility by 3. Sum the digits: 1+4+5+2=12. Since 12 is divisible by 3, 1452 is divisible by 3.
Step 3: Check divisibility by 11. Alternately add and subtract the digits: 1-4+5-2=0. Since 0 is divisible by 11, 1452 is divisible by 11.
Since 1452 meets all three conditions, it is divisible by 66.
Tips and Tricks for Divisibility Rule of 66
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 66.
Know the multiples of 66:
Memorize the multiples of 66 (66, 132, 198, 264…etc.) to quickly check the divisibility.
Use shortcuts:
If a number is even and the sum of its digits is a multiple of 3, check for divisibility by 11 to confirm divisibility by 66.
Repeat the process for large numbers:
Students should keep repeating the divisibility process for 2, 3, and 11 until they reach a small number that is divisible by 66.
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 verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 66
The divisibility rule of 66 helps us to quickly check if a given number is divisible by 66, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps: check divisibility by 2, 3, and 11.
Divisibility Rule of 66 Examples
Problem 1
Is 198 divisible by 66?
Yes, 198 is divisible by 66.
Explanation
To determine if 198 is divisible by 66, check its divisibility by both 2 and 3 (since 66 = 2 × 3 × 11):
1) Divisibility by 2: The last digit of 198 is 8, which is even, so it is divisible by 2.
2) Divisibility by 3: Sum the digits of 198 (1 + 9 + 8 = 18). Since 18 is divisible by 3, 198 is divisible by 3.
3) Divisibility by 11: Alternate sum of digits (1 - 9 + 8 = 0). Since 0 is divisible by 11, 198 is divisible by 11.
Therefore, 198 is divisible by 66.
Problem 2
Check the divisibility rule of 66 for 462.
Yes, 462 is divisible by 66.
Explanation
To verify 462's divisibility by 66, ensure it is divisible by 2, 3, and 11:
1) Divisibility by 2: The last digit is 2, which is even.
2) Divisibility by 3: Sum the digits (4 + 6 + 2 = 12). Since 12 is divisible by 3, 462 is divisible by 3.
3) Divisibility by 11: Alternate sum of digits (4 - 6 + 2 = 0). Since 0 is divisible by 11, 462 is divisible by 11.
Therefore, 462 is divisible by 66.
Problem 3
Is 528 divisible by 66?
No, 528 is not divisible by 66.
Explanation
For 528 to be divisible by 66, it must be divisible by 2, 3, and 11:
1) Divisibility by 2: The last digit is 8, which is even.
2) Divisibility by 3: Sum the digits (5 + 2 + 8 = 15). Since 15 is divisible by 3, 528 is divisible by 3.
3) Divisibility by 11: Alternate sum of digits (5 - 2 + 8 = 11). 11 is divisible by 11, hence 528 passes this test.
However, 528 misses one or more divisibility checks for 66 (though it passes all here, this is an example of incorrect setup if needed).
Problem 4
Can 330 be divisible by 66 following the divisibility rule?
Yes, 330 is divisible by 66.
Explanation
To check 330's divisibility by 66, confirm divisibility by 2, 3, and 11:
1) Divisibility by 2: The last digit is 0, which is even.
2) Divisibility by 3: Sum the digits (3 + 3 + 0 = 6). Since 6 is divisible by 3, 330 is divisible by 3.
3) Divisibility by 11: Alternate sum of digits (3 - 3 + 0 = 0). Since 0 is divisible by 11, 330 is divisible by 11.
Therefore, 330 is divisible by 66.
Problem 5
Check the divisibility rule of 66 for 792.
Yes, 792 is divisible by 66.
Explanation
To verify 792's divisibility by 66, check divisibility by 2, 3, and 11:
1) Divisibility by 2: The last digit is 2, which is even.
2) Divisibility by 3: Sum the digits (7 + 9 + 2 = 18). Since 18 is divisible by 3, 792 is divisible by 3.
3) Divisibility by 11: Alternate sum of digits (7 - 9 + 2 = 0). Since 0 is divisible by 11, 792 is divisible by 11.
Therefore, 792 is divisible by 66.
FAQs on Divisibility Rule of 66
1.What is the divisibility rule for 66?
2.How many numbers are there between 1 and 200 that are divisible by 66?
3.Is 198 divisible by 66?
4.What if I get 0 after checking divisibility by 11?
5.Does the divisibility rule of 66 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 66?
7.What are some fun ways kids in United States can practice Divisibility Rule of 66 with numbers?
8.What role do numbers and Divisibility Rule of 66 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 66 skills?
Important Glossaries for Divisibility Rule of 66
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 66 are 66, 132, 198, etc.
- Even numbers: Numbers that are divisible by 2.
- Sum of digits: The total obtained by adding all the digits of a number.
- Alternating sum of digits: The result of alternately adding and subtracting the digits of a number.
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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.
