Divisibility Rule of 27
2026-02-28 10:32 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 27.

What is the Divisibility Rule of 27?

The divisibility rule for 27 is a method by which we can find out if a number is divisible by 27 or not without using the division method. Check whether 486 is divisible by 27 with the divisibility rule.


Step 1: Find the sum of the digits of the number. Here in 486, the sum is 4+8+6=18.


Step 2: Check if the sum obtained in Step 1 is divisible by 9. If it is, multiply the sum by 3 to check for divisibility by 27. Here, 18 is divisible by 9 (since 18/9=2), and 18 multiplied by 3 is 54, which is not divisible by 27. Therefore, 486 is not divisible by 27.

Tips and Tricks for Divisibility Rule of 27

Learning the divisibility rule will help kids to master the division. Let’s learn a few tips and tricks for the divisibility rule of 27.

  • Know the multiples of 27: Memorize the multiples of 27 (27, 54, 81, 108, 135, etc.) to quickly check divisibility. If 486 were divisible by 27, 54 would need to be a multiple of 27, which it is not.
     
  • Use the sum of digits: If the sum of the digits is not divisible by 9, you can immediately determine that the number is not divisible by 27.
     
  • Break down the problem: For large numbers, break them down into manageable parts, find the sum of digits for each part, and check divisibility by 27.
     
  • 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 to verify and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 27

The divisibility rule of 27 helps us to quickly check if the given number is divisible by 27, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you to understand.

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Problem 1

Is 729 divisible by 27?

Okay, lets begin

Yes, 729 is divisible by 27.

Explanation

To check if 729 is divisible by 27, use the divisibility rule for 27:


1) Split the number into groups of three digits from the right: 729.


2) Since it’s a three-digit number, consider the number itself.


3) 729 / 27 = 27, which is an integer. Therefore, 729 is divisible by 27.

Well explained 👍

Problem 2

Check the divisibility rule of 27 for 1458.

Okay, lets begin

Yes, 1458 is divisible by 27.

Explanation

To determine if 1458 is divisible by 27:


1) Split the number into groups of three digits: 1 and 458.


2) Consider each group. Since 1 is less than 27, focus on 458.


3) Calculate 458 / 27 = 17, which is an integer. Therefore, 1458 is divisible by 27.

Well explained 👍

Problem 3

Is -2916 divisible by 27?

Okay, lets begin

Yes, -2916 is divisible by 27.

Explanation

To check if -2916 is divisible by 27, ignore the negative sign:


1) Split the number into groups of three digits: 2 and 916.


2) Consider each group. Since 2 is less than 27, focus on 916.


3) Calculate 916 / 27 = 34, which is an integer. Therefore, 2916 is divisible by 27, and so is -2916.

Well explained 👍

Problem 4

Can 1234 be divisible by 27 following the divisibility rule?

Okay, lets begin

No, 1234 isn't divisible by 27.

Explanation

To check if 1234 is divisible by 27:


1) Split the number into groups of three digits: 1 and 234.


2) Consider each group. Since 1 is less than 27, focus on 234.


3) Calculate 234 / 27, which gives approximately 8.67, not an integer.

Therefore, 1234 is not divisible by 27.

Well explained 👍

Problem 5

Check the divisibility rule of 27 for 5832.

Okay, lets begin

Yes, 5832 is divisible by 27.

Explanation

To check if 5832 is divisible by 27:


1) Split the number into groups of three digits: 5 and 832.


2) Consider each group. Since 5 is less than 27, focus on 832.

3) Calculate 832 / 27 = 30.81, which rounds up to 31, which is not an integer. There was an error in calculation. Recalculate using 5832 / 27 = 216, which is an integer. Therefore, 5832 is divisible by 27.

Well explained 👍

FAQs on Divisibility Rule of 27

1.What is the divisibility rule for 27?

The divisibility rule for 27 involves finding the sum of the digits of the number, checking if it is divisible by 9, and then verifying if multiplying that result by 3 gives a multiple of 27.

2.How many numbers are there between 1 and 100 that are divisible by 27?

There are 3 numbers between 1 and 100 that are divisible by 27. The numbers are 27, 54, and 81.

3.Is 54 divisible by 27?

Yes, because 54 is a multiple of 27 (27 × 2 = 54).

4.What if I get a sum that is divisible by 9 but not by 27?

In such a case, the number is not divisible by 27. You need to multiply the sum by 3 and check if the result is a multiple of 27.

5.Does the divisibility rule of 27 apply to all integers?

Yes, the divisibility rule of 27 applies to all integers.

Important Glossaries for Divisibility Rule of 27

  • Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
     
  • Sum of digits: The result obtained by adding all the digits of a number.
     
  • Multiple: A number that can be divided by another number without leaving a remainder.
     
  • Integers: Whole numbers, including negative numbers and zero.
     
  • Verification: The process of confirming the accuracy of a calculation or result.

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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.