Divisibility Rule of 123
2026-02-28 15:53 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 123.

What is the Divisibility Rule of 123?

The divisibility rule for 123 is a method by which we can find out if a number is divisible by 123 or not without using the division method. Check whether 492 is divisible by 123 with the divisibility rule.

Step 1: Add the digits of the number together. For 492, add 4 + 9 + 2 = 15.


Step 2: Check if the sum obtained in Step 1 is divisible by 3. Since 15 is divisible by 3, the original number might be divisible by 123.


Step 3: Divide the original number by 123 to verify. 492 ÷ 123 = 4. As there is no remainder, 492 is divisible by 123.

Tips and Tricks for Divisibility Rule of 123

Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 123.

  • Know the multiples of 123:
    Memorize the multiples of 123 (123, 246, 369, 492…etc.) to quickly check the divisibility. If the division of the original number by 123 results in a whole number, then the number is divisible by 123.
  • Use estimation: If you find large numbers difficult, estimate the closest multiple of 123 and compare the difference. This can help in checking the divisibility quickly.
  • Repeat the process for large numbers: Students should keep repeating the divisibility process with the sum of digits until they reach a small number that is easier to check for divisibility by 3. 

    For example: Check if 6153 is divisible by 123 using the divisibility test.

    Add the digits: 6 + 1 + 5 + 3 = 15.

    Since 15 is divisible by 3, check by division. 6153 ÷ 123 = 50. As there is no remainder, 6153 is divisible by 123.

  • 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 123

The divisibility rule of 123 helps us to quickly check if the given number is divisible by 123, 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 492 divisible by 123?

Okay, lets begin

Yes, 492 is divisible by 123.

Explanation

To determine if 492 is divisible by 123, we can follow these steps:


1) Take the first three digits of the number, which is the whole number in this case, 492.


2) Divide 492 by 123. 


3) The result is exactly 4, with no remainder. Therefore, 492 is divisible by 123.

Well explained 👍

Problem 2

Check the divisibility rule of 123 for 615.

Okay, lets begin

Yes, 615 is divisible by 123.

Explanation

To check if 615 is divisible by 123:


1) Consider the whole number, 615.


2) Divide 615 by 123.


3) The result is exactly 5, with no remainder. Thus, 615 is divisible by 123.

Well explained 👍

Problem 3

Is -246 divisible by 123?

Okay, lets begin

Yes, -246 is divisible by 123.

Explanation

To determine if -246 is divisible by 123, we ignore the negative sign and check the absolute value:


1) Take the absolute value, which is 246.


2) Divide 246 by 123.


3) The result is exactly 2, with no remainder. Therefore, -246 is divisible by 123.

Well explained 👍

Problem 4

Can 370 be divisible by 123 following the divisibility rule?

Okay, lets begin

No, 370 isn't divisible by 123.

Explanation

To check if 370 is divisible by 123:


1) Consider the whole number, 370.


2) Divide 370 by 123.


3) The result is approximately 3.008, which is not an integer. Therefore, 370 is not divisible by 123.

Well explained 👍

Problem 5

Check the divisibility rule of 123 for 738.

Okay, lets begin

Yes, 738 is divisible by 123.

Explanation

To check the divisibility of 738 by 123:


1) Take the whole number, 738.


2) Divide 738 by 123.


3) The result is exactly 6, with no remainder. Thus, 738 is divisible by 123.

Well explained 👍

FAQs on Divisibility Rule of 123

1. What is the divisibility rule for 123?

The divisibility rule for 123 involves adding the digits of the number and checking if the sum is divisible by 3, then verifying by dividing the original number by 123.

2.How many numbers are there between 1 and 1000 that are divisible by 123?

There are 8 numbers that can be divided by 123 between 1 and 1000. The numbers are 123, 246, 369, 492, 615, 738, 861, 984.

3.Is 246 divisible by 123?

Yes, because 246 is a multiple of 123 (123 × 2 = 246).

4.What if I get 0 after dividing?

If you get 0 as the remainder after dividing, it is considered that the number is divisible by 123.

5.Does the divisibility rule of 123 apply to all integers?

Yes, the divisibility rule of 123 applies to all integers.

Important Glossary for Divisibility Rule of 123

  • Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
  • Multiple: A multiple is the result of multiplying a number by an integer. For example, multiples of 123 are 123, 246, 369, 492, etc.
  • Sum of digits: The result of adding all the digits in a number together. 
  • Estimation: A method used to find an approximate answer, which can be useful in determining divisibility quickly.
  • Verification: The process of confirming that a calculation or result is correct, often by using an alternate method such as division.

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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.