Divisibility Rule of 231
2026-02-28 09:47 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 231.

What is the Divisibility Rule of 231?

The divisibility rule for 231 is a method by which we can find out if a number is divisible by 231 without using the division method. Check whether 693 is divisible by 231 with the divisibility rule.  


Step 1: Check if the number is divisible by 3. Add the digits of the number. For 693, 6 + 9 + 3 = 18, which is divisible by 3.


Step 2: Check if the number is divisible by 7. Use the rule for 7 (if needed, see the previous section on divisibility by 7).


Step 3: Check if the number is divisible by 11. For 693, subtract the sum of the digits in odd positions from the sum of the digits in even positions: (6 + 3) - 9 = 0, which is divisible by 11.


Step 4: If a number is divisible by 3, 7, and 11, then it is divisible by 231. Since 693 is divisible by 3, 7, and 11, it is divisible by 231.
 

Tips and Tricks for Divisibility Rule of 231

Knowing divisibility rules helps kids master division. Let’s learn a few tips and tricks for divisibility rule of 231.

Know the rules for 3, 7, and 11:


Memorize the rules for divisibility by 3, 7, and 11 to quickly check divisibility by 231.

Break down large problems:


When dealing with large numbers, break them down into smaller parts to apply the divisibility rules more easily.

Repeat the process for large numbers:


Keep repeating the divisibility process until you reach a clear conclusion about divisibility by 231.

Use the division method to verify:


Use the division method as a way to verify and cross-check your results. This will help verify and also enhance learning.

Common Mistakes and How to Avoid Them in Divisibility Rule of 231

The divisibility rule of 231 helps us quickly check if a given number is divisible by 231, but common mistakes can lead to incorrect results. Here, we understand some common mistakes and how to avoid them.
 

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Problem 1

Is 693 divisible by 231?

Okay, lets begin

Yes, 693 is divisible by 231.  
 

Explanation

 To check if 693 is divisible by 231, follow these steps:  


1) Divide 693 by 231, which gives 3.  


2) Since the quotient is an integer with no remainder, 693 is divisible by 231.
 

Well explained 👍

Problem 2

Check the divisibility rule of 231 for 1155.

Okay, lets begin

Yes, 1155 is divisible by 231

Explanation

To verify if 1155 is divisible by 231, use the following steps:  


1) Divide 1155 by 231, which results in 5.  


2) The division results in a whole number with no remainder, confirming that 1155 is divisible by 231.

Well explained 👍

Problem 3

Is 462 divisible by 231?

Okay, lets begin

Yes, 462 is divisible by 231.  

Explanation

To determine if 462 is divisible by 231, follow these steps:  


1) Divide 462 by 231, and you get 2.  


2) The quotient is an integer with no remainder, indicating that 462 is divisible by 231.
 

Well explained 👍

Problem 4

Can 770 be divisible by 231 following the divisibility rule?

Okay, lets begin

 No, 770 is not divisible by 231.  
 

Explanation

 To assess if 770 is divisible by 231, use the following steps:  


1) Divide 770 by 231, which yields approximately 3.333.  


2) Since the result is not a whole number, 770 is not divisible by 231.
 

Well explained 👍

Problem 5

Check the divisibility rule of 231 for 1386.

Okay, lets begin

Yes, 1386 is divisible by 231.  
 

Explanation

 To confirm if 1386 is divisible by 231, follow these steps:  


1) Divide 1386 by 231, which gives exactly 6.  


2) Since the division yields a whole number with no remainder, 1386 is divisible by 231.
 

Well explained 👍

FAQs on Divisibility Rule of 231

1. What is the divisibility rule for 231?

 A number is divisible by 231 if it is divisible by 3, 7, and 11.
 

2.How many numbers are there between 1 and 1000 that are divisible by 231?

To find the numbers, divide 1000 by 231. The largest integer less than the quotient is the count. (1000 / 231 ≈ 4.33, so there are 4 numbers: 231, 462, 693, and 924).
 

3. Is 924 divisible by 231?

Yes, because 924 is divisible by 3, 7, and 11.
 

4.What if I get 0 after checking divisibility by each factor?

If you determine divisibility by 3, 7, and 11, the number is divisible by 231.
 

5.Does the divisibility rule of 231 apply to all integers?

Yes, the divisibility rule of 231 applies to all integers.
 

Important Glossaries for Divisibility Rule of 231

  • Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing division.
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 231 are 231, 462, 693, etc.
  • Integer: Whole numbers, including negative numbers and zero.
  • Summation: The process of adding numbers together.
  • Verification: The process of confirming that a result is correct, often by using a different method.
     

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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.