Divisibility Rule of 6
2026-02-28 00:55 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 6.

What is the Divisibility Rule of 6?

The divisibility rule for 6 is a method by which we can find out if a number is divisible by 6 or not without using the division method. A number is divisible by 6 if it is divisible by both 2 and 3.

Check whether 204 is divisible by 6 with the divisibility rule.

Step 1: Check if the number is even. Since 204 ends with 4, which is even, it is divisible by 2.

Step 2: Add the digits of the number. 2 + 0 + 4 = 6.

Step 3: Check if the sum from Step 2 is a multiple of 3. Since 6 is a multiple of 3, 204 is divisible by 3.

Since 204 is divisible by both 2 and 3, it is divisible by 6.

Tips and Tricks for Divisibility Rule of 6

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 6.

Know the multiples of 6:

Memorize the multiples of 6 (6, 12, 18, 24, 30, etc.) to quickly check the divisibility.

Check divisibility by 2 and 3:

For a number to be divisible by 6, ensure it's divisible by both 2 (even numbers) and 3 (sum of digits is a multiple of 3).

Repeat the process for larger numbers:

Students should keep repeating the process of checking divisibility by 2 and 3 until they reach a conclusion.

Use the division method to verify:

Students can use the division method to verify and cross-check their results. This will help them confirm and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 6

The divisibility rule of 6 helps us quickly check if a given number is divisible by 6, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.

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Problem 1

Can the number 234 be divided by 6 without leaving a remainder?

Okay, lets begin

Yes, 234 is divisible by 6.

Explanation

To verify divisibility by 6, a number must be divisible by both 2 and 3.
1) Check divisibility by 2: The last digit is 4, which is even. Therefore, 234 is divisible by 2.
2) Check divisibility by 3: Sum the digits, 2 + 3 + 4 = 9. Since 9 is divisible by 3, 234 is also divisible by 3.
Since 234 satisfies both conditions, it is divisible by 6.
 

Well explained 👍

Problem 2

Is 525 divisible by 6?

Okay, lets begin

No, 525 is not divisible by 6.

Explanation

To determine divisibility by 6, we check for divisibility by both 2 and 3.
1) Check divisibility by 2: The last digit is 5, which is odd. Therefore, 525 is not divisible by 2.
Since 525 is not divisible by 2, it cannot be divisible by 6, even though 525 is divisible by 3 (5 + 2 + 5 = 12, and 12 is divisible by 3).

Well explained 👍

Problem 3

Determine if -360 is divisible by 6.

Okay, lets begin

Yes, -360 is divisible by 6.

Explanation

The criteria for divisibility by 6 are divisibility by both 2 and 3.
1) Check divisibility by 2: The last digit is 0, which is even, so -360 is divisible by 2.
2) Check divisibility by 3: Sum the digits without considering the negative sign, 3 + 6 + 0 = 9. Since 9 is divisible by 3, -360 is also divisible by 3.
Therefore, -360 meets both conditions and is divisible by 6.

Well explained 👍

Problem 4

Can the number 157 be divided by 6 according to the divisibility rule?

Okay, lets begin

No, 157 is not divisible by 6.

Explanation

For divisibility by 6, the number must be divisible by both 2 and 3.
1) Check divisibility by 2: The last digit is 7, which is odd, so 157 is not divisible by 2.
Since 157 is not divisible by 2, it cannot be divisible by 6, even though 1 + 5 + 7 = 13, and 13 is not divisible by 3.
 

Well explained 👍

Problem 5

Is the number 480 divisible by 6?

Okay, lets begin

Yes, 480 is divisible by 6.

Explanation

We need to verify divisibility by both 2 and 3.
1) Check divisibility by 2: The last digit is 0, which is even, so 480 is divisible by 2.
2) Check divisibility by 3: Sum the digits, 4 + 8 + 0 = 12. Since 12 is divisible by 3, 480 is also divisible by 3.
Since 480 is divisible by both 2 and 3, it is divisible by 6.
 

Well explained 👍

FAQs on Divisibility Rule of 6

1.What is the divisibility rule for 6?

The divisibility rule for 6 is that a number must be divisible by both 2 (even numbers) and 3 (the sum of its digits is a multiple of 3).

2.How many numbers are there between 1 and 100 that are divisible by 6?

There are 16 numbers that can be divided by 6 between 1 and 100. The numbers are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.

3.Is 36 divisible by 6?

Yes, because 36 is even and the sum of its digits (3 + 6 = 9) is a multiple of 3.

4.What if I get 0 after adding the digits?

If the sum of the digits is 0, the number is divisible by 3 (and hence by 6 if it is also even).
 

5.Does the divisibility rule of 6 apply to all integers?

Yes, the divisibility rule of 6 applies to all integers.

Important Glossary for Divisibility Rule of 6

  • Divisibility Rule: The set of rules used to determine whether a number is divisible by another number without performing division.
  • Even Numbers: Numbers that end with 0, 2, 4, 6, or 8, which are divisible by 2.
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 6 are 6, 12, 18, 24, etc.
  • Sum of Digits: The total obtained by adding all the digits of a number.
  • Integer: A whole number that can be positive, negative, or zero.

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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.