Divisibility Rule of 378
2026-02-28 01:31 Diff
https://brightchamps.com/en-us/math/numbers/divisibility-rule-of-378

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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 378.

What is the Divisibility Rule of 378?

The divisibility rule for 378 is a method by which we can determine if a number is divisible by 378 without using the division method. Check whether 756 is divisible by 378 with the divisibility rule.
 

Step 1: Check if the number is divisible by 2. Here, 756 ends in 6, which is even, so it is divisible by 2.
 

Step 2: Check if the number is divisible by 3. Add the digits of 756 (7 + 5 + 6 = 18), which is divisible by 3, so 756 is divisible by 3.
 

Step 3: Check if the number is divisible by 7. Follow the divisibility rule for 7: double the last digit (6 x 2 = 12) and subtract from the rest of the number (75 - 12 = 63), which is divisible by 7. Therefore, 756 is divisible by 7.
 

Since 756 is divisible by 2, 3, and 7, it is divisible by 378 as well.
 

Tips and Tricks for Divisibility Rule of 378

Learn divisibility rules to help master division. Let’s explore a few tips and tricks for the divisibility rule of 378.
 

  • Know the multiples of 378: Memorize the multiples of 378 (378, 756, 1134, etc.) to quickly check divisibility. If the number matches a multiple, it is divisible by 378.
     
  • Use the divisibility rules for 2, 3, and 7: Remember, a number divisible by 378 must be divisible by 2, 3, and 7 simultaneously.
     
  • Repeat the process for large numbers: For larger numbers, repeat the divisibility tests until you find a small number that meets all the criteria.
     
  • 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 378

The divisibility rule of 378 helps us quickly check if a given number is divisible by 378, 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

Is 756 divisible by 378?

Okay, lets begin

Yes, 756 is divisible by 378. 

Explanation

The number 756 is double 378. Therefore, 756 is divisible by 378 as 378 x 2 = 756.

Well explained 👍

Problem 2

Check the divisibility rule of 378 for 1134.

Okay, lets begin

Yes, 1134 is divisible by 378. 

Explanation

To verify the divisibility of 1134 by 378, let's divide:  

1134 ÷ 378 = 3.  


Since the division results in an integer, 1134 is divisible by 378.
 

Well explained 👍

Problem 3

Is -1512 divisible by 378?

Okay, lets begin

Yes, -1512 is divisible by 378. 

Explanation

For negative numbers, consider the absolute value and then check divisibility:  

1512 ÷ 378 = 4.  

Since the division results in an integer, -1512 is divisible by 378.

Well explained 👍

Problem 4

Can 500 be divisible by 378 following the divisibility rule?

Okay, lets begin

No, 500 isn't divisible by 378.

Explanation

Check the division result:  

500 ÷ 378 ≈ 1.322.  

Since the result is not an integer, 500 is not divisible by 378.

Well explained 👍

Problem 5

Check the divisibility rule of 378 for 3024.

Okay, lets begin

Yes, 3024 is divisible by 378.

Explanation

Divide to verify:  

3024 ÷ 378 = 8.  

Since the division results in an integer, 3024 is divisible by 378.

Well explained 👍

FAQs on Divisibility Rule of 378

1.What is the divisibility rule for 378?

The divisibility rule for 378 requires a number to be divisible by 2, 3, and 7 simultaneously.

2.How many numbers between 1 and 1000 are divisible by 378?

There are 2 numbers (378 and 756) between 1 and 1000 that are divisible by 378.

3.Is 1134 divisible by 378?

Yes, because 1134 is divisible by 2, 3, and 7.

4.What if I get 0 after subtracting when checking for 7?

If you get 0 after subtracting, it indicates the number is divisible by 7.

5.Does the divisibility rule of 378 apply to all integers?

Yes, the divisibility rule of 378 applies to all integers.

Important Glossary for Divisibility Rule of 378

  • Divisibility rule: A set of guidelines to determine if a number can be divided by another without remainder.
     
  • Multiple: The result of multiplying a number by an integer. For example, multiples of 378 are 378, 756, etc.
     
  • Integer: Whole numbers, including negative numbers and zero.
     
  • Subtraction: A mathematical operation of finding the difference between numbers.
     
  • Sum of digits: The total obtained by adding all the digits in a number, used to check divisibility by 3.
     

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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.