Divisibility Rule of 30
2026-02-28 13:38 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 30.

What is the Divisibility Rule of 30?

The divisibility rule for 30 is a method by which we can find out if a number is divisible by 30 or not without using the division method. A number is divisible by 30 if it is divisible by 2, 3, and 5. Check whether 180 is divisible by 30 with the divisibility rule.

Step 1: Check divisibility by 2. A number is divisible by 2 if its last digit is even. Here, 180 ends with 0, which 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. Here, 1+8+0=9, which is divisible by 3.

Step 3: Check divisibility by 5. A number is divisible by 5 if its last digit is 0 or 5. Here, 180 ends with 0, so it is divisible by 5.

Since 180 is divisible by 2, 3, and 5, it is divisible by 30.

Tips and Tricks for Divisibility Rule of 30

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 30.

  • Know the multiples of 30: Memorize the multiples of 30 (30, 60, 90, 120, etc.) to quickly check divisibility.
     
  • Check the divisibility by each factor: Make sure to check divisibility by 2, 3, and 5 separately, as a number must be divisible by all three to be divisible by 30.
     
  • Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 30

The divisibility rule of 30 helps us quickly check if a given number is divisible by 30, 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

A farmer has 210 apples and wants to pack them into boxes containing 30 apples each. Can he do this evenly without any apples left over?

Okay, lets begin

Yes, 210 is divisible by 30.

Explanation

To determine if 210 is divisible by 30, we need to check divisibility by 2, 3, and 5.  


1) The last digit is 0, so it is divisible by 2.  


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


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


Since 210 is divisible by 2, 3, and 5, it is divisible by 30.

Well explained 👍

Problem 2

A theater has 360 seats and wants to arrange them in rows of 30 seats each. Can this be done without leaving any seats empty or unused?

Okay, lets begin

Yes, 360 is divisible by 30.

Explanation

To verify if 360 is divisible by 30, we check for divisibility by 2, 3, and 5.  


1) The last digit is 0, so it is divisible by 2.  


2) The sum of the digits is 3 + 6 + 0 = 9, which is divisible by 3.  


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


Since 360 meets all three conditions, it is divisible by 30.

Well explained 👍

Problem 3

A baker is preparing 270 cupcakes and wants to place them on trays holding 30 cupcakes each. Can he achieve this with no cupcakes left over?

Okay, lets begin

Yes, 270 is divisible by 30.

Explanation

We check the divisibility of 270 by 2, 3, and 5:  


1) The last digit is 0, so it is divisible by 2.  


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


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


Therefore, 270 is divisible by 30.

Well explained 👍

Problem 4

A company prints 150 flyers and wants to distribute them in packs of 30. Can they do this without any leftover flyers?

Okay, lets begin

Yes, 150 is divisible by 30.

Explanation

To confirm, we check divisibility by 2, 3, and 5:  


1) The last digit is 0, so it is divisible by 2.  


2) The sum of the digits is 1 + 5 + 0 = 6, which is divisible by 3.

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


Since 150 satisfies all conditions, it is divisible by 30.

Well explained 👍

Problem 5

A school has 480 pencils and wants to organize them into bundles of 30. Will this result in any extra pencils?

Okay, lets begin

Yes, 480 is divisible by 30.

Explanation

We need to check divisibility by 2, 3, and 5:  


1) The last digit is 0, so it is divisible by 2.  


2) The sum of the digits is 4 + 8 + 0 = 12, which is divisible by 3.  


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


Therefore, 480 is divisible by 30.

Well explained 👍

FAQs on Divisibility Rule of 30

1.What is the divisibility rule for 30?

The divisibility rule for 30 is checking if a number is divisible by 2, 3, and 5.

2.How many numbers are there between 1 and 200 that are divisible by 30?

There are 6 numbers that can be divided by 30 between 1 and 200. The numbers are 30, 60, 90, 120, 150, and 180.

3.Is 150 divisible by 30?

Yes, because 150 is divisible by 2, 3, and 5.

4.What if one of the checks fails?

If any one of the checks for divisibility by 2, 3, or 5 fails, the number is not divisible by 30.

5.Does the divisibility rule of 30 apply to all integers?

Yes, the divisibility rule of 30 applies to all integers.

Important Glossaries for Divisibility Rule of 30

  • Divisibility rule: A set of rules used to determine whether a number is divisible by another number without performing division.
     
  • Multiples: The results we get after multiplying a number by an integer. For example, multiples of 30 are 30, 60, 90, etc.
     
  • Factors: Numbers that divide another number exactly without leaving a remainder. For 30, the factors are 1, 2, 3, 5, 6, 10, 15, and 30.
     
  • Even number: A number divisible by 2, such as 0, 2, 4, 6, and 8.
     
  • Sum of digits: The total obtained by adding all the digits of a number together.

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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.