151 LearnersLast updated on May 26th, 2025
Divisibility Rule of 23
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 23.
What is the Divisibility Rule of 23?
The divisibility rule for 23 is a method by which we can find out if a number is divisible by 23 or not without using the division method. Check whether 276 is divisible by 23 with the divisibility rule.
Step 1: Multiply the last digit of the number by 7, here in 276, 6 is the last digit, multiply it by 7. 6 × 7 = 42.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 27 - 42 = -15.
Step 3: As it is shown that -15 is not a multiple of 23, therefore, the number is not divisible by 23. If the result from Step 2 is a multiple of 23, then the number is divisible by 23.
Tips and Tricks for Divisibility Rule of 23
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 23.
- Know the multiples of 23: Memorize the multiples of 23 (23, 46, 69, 92, 115…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 23, then the number is divisible by 23.
- Use the negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 23.
For example: Check if 4603 is divisible by 23 using the divisibility test. Multiply the last digit by 7, i.e., 3 × 7 = 21.
Subtract the remaining digits excluding the last digit by 21, 460 - 21 = 439. Still, 439 is a large number, hence we will repeat the process again and multiply the last digit by 7, 9 × 7 = 63.
Now subtracting 63 from the remaining numbers excluding the last digit, 43 - 63 = -20. As -20 is not a multiple of 23, 4603 is not divisible by 23.
- 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.
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 23. Know the multiples of 23: Memorize the multiples of 23 (23, 46, 69, 92, 115…etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 23, then the number is divisible by 23. Use the negative numbers: If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number. Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 23. For example: Check if 4603 is divisible by 23 using the divisibility test. Multiply the last digit by 7, i.e., 3 × 7 = 21. Subtract the remaining digits excluding the last digit by 21, 460 - 21 = 439. Still, 439 is a large number, hence we will repeat the process again and multiply the last digit by 7, 9 × 7 = 63. Now subtracting 63 from the remaining numbers excluding the last digit, 43 - 63 = -20. As -20 is not a multiple of 23, 4603 is not divisible by 23. 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.
The divisibility rule of 23 helps us to quickly check if the given number is divisible by 23, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that are multiplying the last digit with 7 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 23.
Divisibility Rule of 23 Examples
Problem 1
Is 276 divisible by 23?
Yes, 276 is divisible by 23.
Explanation
To check if 276 is divisible by 23, follow these steps:
1) Multiply the last digit of the number by 7, 6 × 7 = 42.
2) Subtract the result from the remaining digits, excluding the last digit, 27 - 42 = -15.
3) Check if -15 is a multiple of 23. No, but repeat the process until the result is manageable.
4) The eventual result is 0, indicating that 276 is divisible by 23.
Problem 2
Check if 322 is divisible by 23.
No, 322 is not divisible by 23.
Explanation
To determine divisibility, follow the steps:
1) Multiply the last digit by 7, 2 × 7 = 14.
2) Subtract this from the remaining digits, 32 - 14 = 18.
3) Check if 18 is a multiple of 23. No, 18 is not a multiple of 23.
Problem 3
Is -575 divisible by 23?
Yes, -575 is divisible by 23.
Explanation
To check if -575 is divisible by 23:
1) Ignore the negative sign initially. Multiply the last digit by 7, 5 × 7 = 35.
2) Subtract this from the remaining digits, 57 - 35 = 22.
3) Check if 22 is a multiple of 23. No, but after repeating the steps, the result is 0.
Problem 4
Can 529 be divisible by 23 following the divisibility rule?
No, 529 is not divisible by 23.
Explanation
To check if 529 is divisible by 23:
1) Multiply the last digit by 7, 9 × 7 = 63.
2) Subtract this result from the remaining digits, 52 - 63 = -11.
3) Check if -11 is a multiple of 23. It is not, and no further steps will yield divisibility.
Problem 5
Check the divisibility rule of 23 for 8281.
Yes, 8281 is divisible by 23.
Explanation
To determine if 8281 is divisible by 23:
1) Multiply the last digit by 7, 1 × 7 = 7.
2) Subtract this from the remaining digits, 828 - 7 = 821.
3) Repeat the process for 821: 1 × 7 = 7, 82 - 7 = 75.
4) Continue until the result is manageable. The final result is 0, confirming divisibility by 23.
FAQs on Divisibility Rule of 23
1.What is the divisibility rule for 23?
2.How many numbers are there between 1 and 100 that are divisible by 23?
3.Is 92 divisible by 23?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 23 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 23?
7.What are some fun ways kids in United States can practice Divisibility Rule of 23 with numbers?
8.What role do numbers and Divisibility Rule of 23 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 23 skills?
Important Glossaries for Divisibility Rule of 23
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 23 if the divisibility rule confirms it.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 23 are 23, 46, 69, 92, etc.
- Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
- Verification: The process of checking the accuracy of calculations, often using different methods such as actual 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.
