204 LearnersLast updated on May 26th, 2025
Divisibility Rule of 660
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 660.
What is the Divisibility Rule of 660?
The divisibility rule for 660 is a method by which we can determine if a number is divisible by 660 or not without using the division method. To check the divisibility by 660, a number must be divisible by 2, 3, 5, and 11 as 660 is the product of these numbers. Let's break it down:
1. Divisibility by 2: The number must end in an even digit (0, 2, 4, 6, 8).
2. Divisibility by 3: The sum of the digits of the number must be divisible by 3.
3. Divisibility by 5: The number must end in 0 or 5.
4. Divisibility by 11: The difference between the sum of the digits in odd positions and the sum in even positions must be a multiple of 11 or zero.
Check whether 6600 is divisible by 660 with the divisibility rule.
- Divisibility by 2: 6600 ends in 0, which is even.
- Divisibility by 3: Sum of digits = 6 + 6 + 0 + 0 = 12, which is divisible by 3.
- Divisibility by 5: 6600 ends in 0.
- Divisibility by 11: (6 + 0) - (6 + 0) = 0, which is a multiple of 11.
Since 6600 satisfies all these conditions, it is divisible by 660.
Tips and Tricks for Divisibility Rule of 660
Learn the divisibility rule to master division. Here are a few tips and tricks for the divisibility rule of 660:
- Memorize the rules for 2, 3, 5, and 11: Knowing the individual rules helps in quickly checking divisibility by 660.
- Check in sequence: Start with easier checks like divisibility by 5 and 2, then move to 3 and 11.
- Simplify large numbers: Break down larger numbers into blocks to apply the rules more easily.
- Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This helps in verification and learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 660
The divisibility rule of 660 helps us quickly check if a given number is divisible by 660, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them:
Mistake 1
Not checking all conditions.
Ensure all four conditions (divisibility by 2, 3, 5, 11) are satisfied.
Mistake 2
Miscalculating sums or differences.
Carefully calculate the sums of digits for 3 and differences for 11.
Mistake 3
Ignoring the divisibility by 11 condition.
Always include this step, even if the other conditions are satisfied.
Mistake 4
Confusing divisibility rules of smaller factors.
Practice each rule separately to avoid confusion.
Mistake 5
Forgetting to check the number ends in 0 or 5 for divisibility by 5.
Always start with this simple check.
Divisibility Rule of 660 Examples
Problem 1
Is 3960 divisible by 660?
Yes, 3960 is divisible by 660.
Explanation
To check if 3960 is divisible by 660, we need to verify divisibility by 2, 3, 5, and 11 (since 660 = 2 × 3 × 5 × 11).
1) The number 3960 is even, so it is divisible by 2.
2) Sum of digits is 3 + 9 + 6 + 0 = 18, which is divisible by 3.
3) The last digit is 0, so it is divisible by 5.
4) The alternating sum of digits is (3 + 6) - (9 + 0) = 9 - 9 = 0, which is divisible by 11.
Since 3960 is divisible by 2, 3, 5, and 11, it is divisible by 660.
Problem 2
Check the divisibility rule of 660 for 8580.
Yes, 8580 is divisible by 660.
Explanation
To check divisibility by 660, verify divisibility by 2, 3, 5, and 11.
1) The number 8580 is even, so it is divisible by 2.
2) Sum of digits is 8 + 5 + 8 + 0 = 21, which is divisible by 3.
3) The last digit is 0, so it is divisible by 5.
4) The alternating sum of digits is (8 + 8) - (5 + 0) = 16 - 5 = 11, which is divisible by 11.
Since 8580 is divisible by 2, 3, 5, and 11, it is divisible by 660.
Problem 3
Is 8712 divisible by 660?
No, 8712 is not divisible by 660.
Explanation
To check divisibility by 660, verify divisibility by 2, 3, 5, and 11.
1) The number 8712 is even, so it is divisible by 2.
2) Sum of digits is 8 + 7 + 1 + 2 = 18, which is divisible by 3.
3) The last digit is 2, so it is not divisible by 5.
Since 8712 is not divisible by 5, it is not divisible by 660.
Problem 4
Can 12,540 be divisible by 660 following the divisibility rule?
Yes, 12,540 is divisible by 660.
Explanation
To check divisibility by 660, verify divisibility by 2, 3, 5, and 11.
1) The number 12,540 is even, so it is divisible by 2.
2) Sum of digits is 1 + 2 + 5 + 4 + 0 = 12, which is divisible by 3.
3) The last digit is 0, so it is divisible by 5.
4) The alternating sum of digits is (1 + 5 + 0) - (2 + 4) = 6 - 6 = 0, which is divisible by 11.
Since 12,540 is divisible by 2, 3, 5, and 11, it is divisible by 660.
Problem 5
Check the divisibility rule of 660 for 7920.
Yes, 7920 is divisible by 660.
Explanation
To check divisibility by 660, verify divisibility by 2, 3, 5, and 11.
1) The number 7920 is even, so it is divisible by 2.
2) Sum of digits is 7 + 9 + 2 + 0 = 18, which is divisible by 3.
3) The last digit is 0, so it is divisible by 5.
4) The alternating sum of digits is (7 + 2) - (9 + 0) = 9 - 9 = 0, which is divisible by 11.
Since 7920 is divisible by 2, 3, 5, and 11, it is divisible by 660.
FAQs on Divisibility Rule of 660
1.What is the divisibility rule for 660?
2.Is 1320 divisible by 660?
3.How can I verify if a number is divisible by 660?
4.Can negative numbers be checked with these rules?
5.What if a number is divisible by 2, 3, and 5 but not 11?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 660?
7.What are some fun ways kids in United States can practice Divisibility Rule of 660 with numbers?
8.What role do numbers and Divisibility Rule of 660 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 660 skills?
Important Glossaries for Divisibility Rule of 660
- Divisibility Rule: A set of rules used to determine whether a number is divisible by another number without division.
- Multiples: The results obtained when a number is multiplied by integers.
- Sum of Digits: The total value obtained by adding all digits in a number.
- Even Number: A number ending in 0, 2, 4, 6, or 8.
- Difference of Sums: The result from subtracting the sum of digits in even positions from the sum of digits in odd positions.
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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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