151 LearnersLast updated on May 26th, 2025
Divisibility Rule of 972
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 972.
What is the Divisibility Rule of 972?
The divisibility rule for 972 is a method by which we can find out if a number is divisible by 972 or not without using the division method. Check whether 58320 is divisible by 972 with the divisibility rule.
Step 1: Check if the number is divisible by 2, 3, and 9. A number is divisible by 972 if it is divisible by all three of these numbers.
Step 2: For divisibility by 2, the last digit must be even. In 58320, 0 is even.
Step 3: For divisibility by 3, the sum of the digits must be divisible by 3. Sum of digits: 5+8+3+2+0=18, and 18 is divisible by 3.
Step 4: For divisibility by 9, the sum of the digits must be divisible by 9. The sum of digits is 18, and 18 is divisible by 9.
Since 58320 is divisible by 2, 3, and 9, it is divisible by 972.
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Tips and Tricks for Divisibility Rule of 972
Learn divisibility rules to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 972.
Know the multiples of 972:
Memorize the multiples of 972 (972, 1944, 2916, 3888, etc.) to quickly check divisibility. If the number is a multiple of 972, it is divisible by 972.
Use prime factorization:
Understand that 972 = 2^2 × 3^5. Verify each factor’s divisibility to confirm divisibility by 972.
Repeat the process for large numbers:
For large numbers, check divisibility by 2, 3, and 9 separately and repeat if necessary.
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 972
The divisibility rule of 972 helps us to quickly check if the given number is divisible by 972, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps for checking divisibility by 2, 3, and 9
Mistake 2
Forgetting to check for all factors.
Ensure the number is divisible by 2, 3, and 9.
Mistake 3
Not repeating the process when the number is large.
Repeat the process to ensure accuracy, especially with large numbers.
Mistake 4
Ignoring zero in the divisibility rule for 2.
Remember that a number ending in zero is divisible by 2.
Mistake 5
Confusing the steps.
Practice regularly to keep the steps clear in mind.
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Divisibility Rule of 972 Examples
Problem 1
Is 5832 divisible by 972?
Yes, 5832 is divisible by 972.
Explanation
To check if 5832 is divisible by 972, we can apply the divisibility rule specifically for 972.
1) Calculate the sum of the digits: (5 + 8 + 3 + 2 = 18).
2) Check if the sum of the digits (18) is divisible by 9 (since 972 = ( 9 times 108 )).
3) Since 18 is divisible by 9, further check divisibility by 108.
4) Since 5832 divided by 972 results in an integer (6), 5832 is divisible by 972.
Problem 2
Check the divisibility of 34992 by 972.
Yes, 34992 is divisible by 972.
Explanation
To determine if 34992 is divisible by 972, follow these steps:
1) Calculate the sum of the digits: (3 + 4 + 9 + 9 + 2 = 27).
2) Check if 27 is divisible by 9.
3) Since 27 is divisible by 9, check the divisibility of 34992 by 108.
4) Dividing 34992 by 972 results in an integer (36), confirming divisibility by 972.
Problem 3
Is 1944 divisible by 972?
Yes, 1944 is divisible by 972.
Explanation
To verify divisibility of 1944 by 972:
1) Calculate the sum of the digits: (1 + 9 + 4 + 4 = 18).
2) Since 18 is divisible by 9, further check divisibility by 108.
3) Dividing 1944 by 972 yields an integer (2), confirming divisibility by 972.
Problem 4
Can 2916 be divisible by 972?
Yes, 2916 is divisible by 972.
Explanation
For checking the divisibility of 2916 by 972:
1) Calculate the sum of the digits: (2 + 9 + 1 + 6 = 18).
2) 18 is divisible by 9, so check divisibility by 108.
3) 2916 divided by 972 results in an integer (3), confirming divisibility by 972.
Problem 5
Is 4374 divisible by 972?
No, 4374 is not divisible by 972.
Explanation
To check divisibility of 4374 by 972:
1) Calculate the sum of the digits: (4 + 3 + 7 + 4 = 18).
2) Although 18 is divisible by 9, for complete divisibility, check by 108.
3) 4374 divided by 972 does not result in an integer (result is approximately 4.5), thus 4374 is not divisible by 972.
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FAQs on Divisibility Rule of 972
1.What is the divisibility rule for 972?
2.How do you check if a number is divisible by 972?
3.Is 1944 divisible by 972?
4.What if you find a number not divisible by one factor?
5.Does the divisibility rule of 972 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 972?
7.What are some fun ways kids in India can practice Divisibility Rule of 972 with numbers?
8.What role do numbers and Divisibility Rule of 972 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 972 skills?
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Important Glossaries for Divisibility Rule of 972
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: The results we get after multiplying a number by an integer. For example, multiples of 972 are 972, 1944, 2916, etc.
- Factorization: The process of breaking down a number into its constituent prime factors. For example, 972 = 2^2 × 3^5.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Sum of digits: The total obtained by adding all the digits of a number, used in checking divisibility by 3 and 9.
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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
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