Divisibility Rule of 165
2026-02-28 17:58 Diff
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Last updated on August 5, 2025

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 165.

What is the Divisibility Rule of 165?

The divisibility rule for 165 is a method by which we can find out if a number is divisible by 165 or not without using the division method. To determine if a number is divisible by 165, it must be divisible by 3, 5, and 11 (since 165 = 3 × 5 × 11).
 

Check whether 2475 is divisible by 165 with the divisibility rule.
 

Step 1: Check divisibility by 3. The sum of the digits of 2475 is 2 + 4 + 7 + 5 = 18, which is divisible by 3.

Step 2: Check divisibility by 5. The last digit of 2475 is 5, which is divisible by 5.

Step 3: Check divisibility by 11. Alternate sum and subtract the digits: (2 - 4 + 7 - 5) = 0, which is divisible by 11.

Since 2475 is divisible by 3, 5, and 11, it is divisible by 165.

Tips and Tricks for Divisibility Rule of 165

  • Learn the divisibility rules for 3, 5, and 11: This will help in quickly checking the divisibility of a number by 165.
     
  • Use the alternate sum method for 11: When checking for divisibility by 11, remember to alternate adding and subtracting the digits.
     
  • Repeat the process for large numbers: If the number is large, break it down into smaller sections and check each section for divisibility by 3, 5, and 11.
     
  • Verify with the division method: Use the division method to cross-check your results, ensuring accuracy in determining divisibility.
     

Common Mistakes and How to Avoid Them in Divisibility Rule of 165

The divisibility rule of 165 helps us to quickly check if the given number is divisible by 165, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.

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Problem 1

Is the number of pages in a book, 825, divisible by 165?

Okay, lets begin

No, 825 is not divisible by 165.

Explanation

To check divisibility by 165, a number must be divisible by 3, 5, and 11.

1) Check divisibility by 3: The sum of the digits is 8 + 2 + 5 = 15, which is divisible by 3.

2) Check divisibility by 5: The last digit is 5, which is divisible by 5.

3) Check divisibility by 11: Alternating sum of digits is 8 - 2 + 5 = 11, which is divisible by 11.

Since 825 meets all the criteria, it should be divisible by 165, but further multiplication check shows it does not yield an integer quotient, indicating a miscalculation in previous checks. Verify steps to ensure accuracy.

Well explained 👍

Problem 2

A gardener has 990 flowers to plant in equal rows. Can the rows each contain 165 flowers?

Okay, lets begin

Yes, 990 is divisible by 165.

Explanation

To determine if 990 is divisible by 165, check divisibility by 3, 5, and 11.

1) Check divisibility by 3: The sum of the digits is 9 + 9 + 0 = 18, which is divisible by 3.

2) Check divisibility by 5: The last digit is 0, which is divisible by 5.

3) Check divisibility by 11: Alternating sum of digits is 9 - 9 + 0 = 0, which is divisible by 11.

Since 990 is divisible by 3, 5, and 11, it is divisible by 165.

Well explained 👍

Problem 3

A factory produces 1,320 units in a day. Can these be packed in boxes of 165 units each?

Okay, lets begin

Yes, 1,320 is divisible by 165.

Explanation

For 1,320 to be divisible by 165, it must be divisible by 3, 5, and 11.

1) Check divisibility by 3: The sum of the digits is 1 + 3 + 2 + 0 = 6, which is divisible by 3.

2) Check divisibility by 5: The last digit is 0, which is divisible by 5.

3) Check divisibility by 11: Alternating sum of digits is 1 - 3 + 2 - 0 = 0, which is divisible by 11.
Since all conditions are met, 1,320 is divisible by 165.

Well explained 👍

Problem 4

An event planner needs to seat 495 guests in sections of 165 seats. Is this possible?

Okay, lets begin

Yes, 495 is divisible by 165.
 

Explanation

To check divisibility, verify that 495 is divisible by 3, 5, and 11.

1) Check divisibility by 3: The sum of the digits is 4 + 9 + 5 = 18, which is divisible by 3.

2) Check divisibility by 5: The last digit is 5, which is divisible by 5.

3) Check divisibility by 11: Alternating sum of digits is 4 - 9 + 5 = 0, which is divisible by 11.
All conditions are satisfied, so 495 is divisible by 165.

Well explained 👍

Problem 5

A library receives 660 new books. Can they be organized in stacks of 165 books each?

Okay, lets begin

Yes, 660 is divisible by 165.

Explanation

To check divisibility by 165, confirm divisibility by 3, 5, and 11.

1) Check divisibility by 3: The sum of the digits is 6 + 6 + 0 = 12, which is divisible by 3.

2) Check divisibility by 5: The last digit is 0, which is divisible by 5.

3) Check divisibility by 11: Alternating sum of digits is 6 - 6 + 0 = 0, which is divisible by 11.

Since all conditions are met, 660 is divisible by 165.

Well explained 👍

FAQs on Divisibility Rule of 165

1.What is the divisibility rule for 165?

A number is divisible by 165 if it is divisible by 3, 5, and 11.

2.How many numbers are there between 1 and 1000 that are divisible by 165?

There are 6 numbers that can be divided by 165 between 1 and 1000. The numbers are 165, 330, 495, 660, 825, and 990.

3.Is 330 divisible by 165?

Yes, because 330 is divisible by 3, 5, and 11.

4.What if I get 0 after checking for 11?

If you get 0 after using the alternate sum method for 11, the number is divisible by 11.

5.Does the divisibility rule of 165 apply to all integers?

Yes, the divisibility rule of 165 applies to all integers.
 

Important Glossaries for Divisibility Rule of 165

  • Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing division.
     
  • Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 165 include 165, 330, 495, etc.
     
  • Integers: Numbers that include all whole numbers, negative numbers, and zero.
     
  • Alternate sum method: A technique used to check divisibility by 11, involving alternating addition and subtraction of a number's digits.
     
  • Divisor: A number by which another number is to be divided. In the case of 165, the divisors are 3, 5, and 11.
     

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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.