Divisibility Rule of 744
2026-02-28 09:15 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to determine whether a number is divisible by another number without performing actual division. In real life, we can use divisibility rules for quick calculations, evenly dividing items, and organizing things. In this topic, we will learn about the divisibility rule of 744.

What is the Divisibility Rule of 744?

The divisibility rule for 744 is a method by which we can determine if a number is divisible by 744 without directly dividing it. To check whether a number is divisible by 744, it must be divisible by all the prime factors of 744, which are 2, 3, and 31. 

Example: Check whether 1488 is divisible by 744.

First, check for divisibility by 2: The last digit of 1488 is 8, which is even, so it is divisible by 2.

Next, check for divisibility by 3: Add the digits of 1488 (1+4+8+8=21). Since 21 is divisible by 3, 1488 is divisible by 3.

Finally, check for divisibility by 31: Perform direct division to check if 1488 divided by 31 is a whole number. Since it is, 1488 is divisible by 31.

Since 1488 is divisible by 2, 3, and 31, it is also divisible by 744.

Tips and Tricks for Divisibility Rule of 744

Understanding the divisibility rule will help students master division. Here are some tips and tricks for the divisibility rule of 744:

Know the prime factors:

Memorize the prime factors of 744 (2, 3, and 31) to quickly check divisibility. 

Use smaller checks:

Check divisibility by 2 and 3 first before verifying divisibility by 31.

Repeat the process for large numbers:

If the initial checks show divisibility by 2 and 3, proceed to check divisibility by 31 for confirmation.

Use divisibility rules for factors:

Apply divisibility rules for 2, 3, and 31 individually to simplify the process.

Verify with division:

Use direct division to verify results and reinforce learning.

Common Mistakes and How to Avoid Them in Divisibility Rule of 744

The divisibility rule of 744 helps us quickly determine if a number is divisible by 744, but common mistakes can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them:

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Problem 1

Is 1488 divisible by 744?

Okay, lets begin

Yes, 1488 is divisible by 744. 

Explanation

To check if 1488 is divisible by 744, we divide the number directly.  

1) Divide 1488 by 744.  

2) The quotient is 2 and the remainder is 0.  

3) Since there is no remainder, 1488 is divisible by 744.

Well explained 👍

Problem 2

Check the divisibility rule of 744 for 2232.

Okay, lets begin

Yes, 2232 is divisible by 744. 

Explanation

To check if 2232 is divisible by 744, follow these steps:  

1) Divide 2232 by 744.  

2) The quotient is 3, and the remainder is 0.  

3) Since there is no remainder, 2232 is divisible by 744.

Well explained 👍

Problem 3

Is 372 divisible by 744?

Okay, lets begin

No, 372 is not divisible by 744.

Explanation

To check if 372 is divisible by 744, perform the following steps:  

1) Divide 372 by 744.  

2) The quotient is less than 1, indicating that 744 does not fit into 372.  

3) Since 372 is smaller than 744, it cannot be divisible.

Well explained 👍

Problem 4

Can 744 be divisible by 744 following the divisibility rule?

Okay, lets begin

Yes, 744 is divisible by 744.

Explanation

To check if 744 is divisible by 744, simply divide the number by itself.  

1) Divide 744 by 744.  

2) The quotient is 1, and the remainder is 0.  

3) Since there is no remainder, 744 is divisible by 744.

Well explained 👍

Problem 5

Check the divisibility rule of 744 for 2976.

Okay, lets begin

Yes, 2976 is divisible by 744.

Explanation

To check if 2976 is divisible by 744, perform the following calculations:  
1) Divide 2976 by 744.  

2) The quotient is 4, and the remainder is 0.  

3) Since there is no remainder, 2976 is divisible by 744.

Well explained 👍

FAQs on Divisibility Rule of 744

1.What is the divisibility rule for 744?

A number is divisible by 744 if it is divisible by 2, 3, and 31.

2.How many numbers between 1 and 1000 are divisible by 744?

Only the number 744 itself is divisible by 744 between 1 and 1000.

3.Is 1488 divisible by 744?

Yes, because 1488 is divisible by 2, 3, and 31.

4.What if I get a remainder in one of the checks?

If there is a remainder in any check (2, 3, or 31), the number is not divisible by 744.

5.Does the divisibility rule of 744 apply to all integers?

Yes, the divisibility rule applies to all integers.

Important Glossaries for Divisibility Rule of 744

  • Divisibility rule: A set of guidelines used to determine if one number can be evenly divided by another.
  • Prime factors: The prime numbers that multiply together to give a certain number. For 744, these are 2, 3, and 31.
  • Multiples: Numbers obtained by multiplying a number by an integer.
  • Verification: The process of confirming the correctness of a calculation, often through direct division.
  • Integer: Whole numbers, including negative numbers, positive numbers, and 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.