Divisibility Rule of 330
2026-02-28 23:18 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to determine if a number is divisible by another number without using the traditional division method. In real life, divisibility rules help with quick calculations, dividing things evenly, and sorting. In this topic, we will learn about the divisibility rule of 330.

What is the Divisibility Rule of 330?

The divisibility rule for 330 involves checking if a number is divisible by each of the factors of 330 without using the division method. 330 can be broken down into its prime factors: 2, 3, 5, and 11. Therefore, a number is divisible by 330 if it is divisible by each of these factors. Let's check whether 660 is divisible by 330 using this rule.

Step 1: Check divisibility by 2. A number is divisible by 2 if it is even. 660 is even, so it is divisible by 2.

Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 660 is 6 + 6 + 0 = 12, which is divisible by 3.

Step 3: Check divisibility by 5. A number is divisible by 5 if it ends in 0 or 5. 660 ends in 0, so it is divisible by 5.

Step 4: Check divisibility by 11. A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11 (including 0). For 660, (6+0) - 6 = 0, which is a multiple of 11.

Since 660 satisfies all these conditions, it is divisible by 330.

Tips and Tricks for Divisibility Rule of 330

Understanding divisibility rules helps students master division. Here are some tips and tricks for the divisibility rule of 330:

  • Memorize the conditions for each factor: Remember the divisibility rules for 2, 3, 5, and 11 to quickly check if a number is divisible by 330.
  • Use modular arithmetic: If the result of a condition seems unclear, use simple arithmetic or modular arithmetic to verify divisibility.
  • Break it down: For larger numbers, break them into smaller parts and check each part's divisibility by 2, 3, 5, and 11.
  • Use the division method to verify: Verify your result by using the division method to ensure accuracy and to gain a better understanding.

Common Mistakes and How to Avoid Them in Divisibility Rule of 330

The divisibility rule of 330 allows us to quickly determine if a number is divisible by 330, but common mistakes can lead to errors. Understanding these mistakes can help avoid them.

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Problem 1

Is 1980 divisible by 330?

Okay, lets begin

Yes, 1980 is divisible by 330.

Explanation

To check if 1980 is divisible by 330, we need to ensure it meets the divisibility rules for 2, 3, 5, and 11.

1) 1980 is even, so it is divisible by 2.

2) The sum of the digits is 1 + 9 + 8 + 0 = 18, which is divisible by 3.

3) The last digit is 0, so it is divisible by 5.

4) For divisibility by 11, the difference between the sum of the digits in odd positions and even positions is (1 + 8) - (9 + 0) = 9 - 9 = 0, which is divisible by 11.

Since 1980 meets all these criteria, it is divisible by 330.

Well explained 👍

Problem 2

Check the divisibility rule of 330 for 2970.

Okay, lets begin

Yes, 2970 is divisible by 330.

Explanation

To check if 2970 is divisible by 330, we apply the divisibility rules for 2, 3, 5, and 11.

1) 2970 is even, hence divisible by 2.

2) The sum of the digits is 2 + 9 + 7 + 0 = 18, which is divisible by 3.

3) The last digit is 0, indicating divisibility by 5.

4) For 11, the alternating sum is (2 + 7) - (9 + 0) = 9 - 9 = 0, which is divisible by 11.

Therefore, 2970 satisfies all conditions for divisibility by 330.

Well explained 👍

Problem 3

Is -330 divisible by 330?

Okay, lets begin

Yes, -330 is divisible by 330.

Explanation

To determine if -330 is divisible by 330, we consider the positive number 330 and apply the divisibility rules for 2, 3, 5, and 11.

1) 330 is even, so it is divisible by 2.

2) The sum of the digits is 3 + 3 + 0 = 6, which is divisible by 3.

3) The last digit is 0, so it is divisible by 5.

4) For 11, the alternating sum is (3 + 0) - 3 = 3 - 3 = 0, which is divisible by 11.

Thus, -330 is divisible by 330.

Well explained 👍

Problem 4

Can 715 be divisible by 330 following the divisibility rule?

Okay, lets begin

No, 715 isn't divisible by 330.

Explanation

To verify if 715 is divisible by 330, we must check divisibility by 2, 3, 5, and 11.

1) 715 is not even, so it fails the divisibility rule for 2.

2) The sum of the digits is 7 + 1 + 5 = 13, which is not divisible by 3.

3) The last digit is 5, satisfying divisibility by 5.

4) For 11, the alternating sum is (7 + 5) - 1 = 12 - 1 = 11, which is divisible by 11.

Since 715 does not meet all the necessary criteria, it is not divisible by 330.

Well explained 👍

Problem 5

Check the divisibility rule of 330 for 3630.

Okay, lets begin

Yes, 3630 is divisible by 330.

Explanation

To confirm if 3630 is divisible by 330, verify the rules for 2, 3, 5, and 11.

1) 3630 is even, so it satisfies divisibility by 2.

2) The sum of the digits is 3 + 6 + 3 + 0 = 12, which is divisible by 3.

3) The last digit is 0, fulfilling the divisibility rule for 5.

4) For 11, the alternating sum is (3 + 3) - (6 + 0) = 6 - 6 = 0, which is divisible by 11.

Therefore, 3630 meets all criteria and is divisible by 330.

Well explained 👍

FAQs on Divisibility Rule of 330

1.What is the divisibility rule for 330?

A number is divisible by 330 if it is divisible by 2, 3, 5, and 11.

2.How many numbers between 1 and 1000 are divisible by 330?

There are 3 numbers divisible by 330 between 1 and 1000: 330, 660, and 990.

3.Is 990 divisible by 330?

Yes, because 990 is divisible by 2, 3, 5, and 11.

4.What if I get a remainder after checking divisibility by one factor?

 If any factor leaves a remainder, the number is not divisible by 330.

5.Does the divisibility rule of 330 apply to all integers?

Yes, the divisibility rule of 330 applies to all integers.

Important Glossaries for Divisibility Rule of 330

  • Divisibility rule: A set of rules used to determine if a number is divisible by another without division.
  • Prime factors: The prime numbers that multiply together to give the original number. For 330, these are 2, 3, 5, and 11.
  • Even number: A number divisible by 2.
  • Sum of digits: The total obtained by adding all digits of a number, used to check divisibility by 3.
  • Modular arithmetic: A method of arithmetic for integers, where numbers wrap around upon reaching a certain value (the modulus).
     

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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.