230 LearnersLast updated on May 26th, 2025
Divisibility Rule of 97
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 97.
What is the Divisibility Rule of 97?
The divisibility rule for 97 is a method by which we can find out if a number is divisible by 97 or not without using the division method. Check whether 4858 is divisible by 97 with the divisibility rule.
Step 1: Multiply the last digit of the number by 29, here in 4858, 8 is the last digit, multiply it by 29. 8 × 29 = 232.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 485–232 = 253.
Step 3: As it is shown that 253 is a multiple of 97, therefore, the number is divisible by 97. If the result from step 2 isn't a multiple of 97, then the number isn't divisible by 97.
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Tips and Tricks for Divisibility Rule of 97
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 97.
- Know the multiples of 97: Memorize the multiples of 97 (97, 194, 291, … etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 97, then the number is divisible by 97.
- 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 97.
For example: Check if 7823 is divisible by 97 using the divisibility test.
Multiply the last digit by 29, i.e., 3 × 29 = 87. Subtract the remaining digits excluding the last digit by 87, 782–87 = 695. Still, 695 is a large number, hence we will repeat the process again and multiply the last digit by 29, 5 × 29 = 145.
Now subtracting 145 from the remaining numbers excluding the last digit, 69–145 = -76. As -76 is negative, we consider it as 76. As 76 is not a multiple of 97, 7823 is not divisible by 97.
- 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 97
The divisibility rule of 97 helps us to quickly check if the given number is divisible by 97, 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 29 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 97.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number to result in after subtraction. The process should be repeated until we get the smallest number that is divisible by 97.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to the negative values. But divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse the steps or forget the steps. To avoid the error, students should practice regularly.
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Divisibility Rule of 97 Examples
Problem 1
Is 9700 divisible by 97?
Yes, 9700 is divisible by 97.
Explanation
To check if 9700 is divisible by 97, follow these steps:
1) Multiply the last digit of the number by 29, which is a part of the divisibility rule for 97. So, 0 × 29 = 0.
2) Subtract the result from the remaining number excluding the last digit, 970 - 0 = 970.
3) Check if 970 is divisible by 97. Yes, 970 is divisible by 97 (97 × 10 = 970).
Problem 2
Check the divisibility rule of 97 for 485.
No, 485 is not divisible by 97.
Explanation
To check if 485 is divisible by 97, use the rule:
1) Multiply the last digit by 29, 5 × 29 = 145.
2) Subtract the result from the remaining digits, excluding the last digit, 48 - 145 = -97.
3) Check if the result is a multiple of 97. Though we reached -97, it is already the negative form of 97, indicating divisibility. However, since our subtraction exceeded the number of digits, a direct check confirms that 485 is not divisible by 97.
Problem 3
Is -1940 divisible by 97?
Yes, -1940 is divisible by 97.
Explanation
For a negative number -1940, remove the negative sign first:
1) Multiply the last digit by 29, 0 × 29 = 0.
2) Subtract the result from the remaining digits excluding the last digit, 194 - 0 = 194.
3) Check if 194 is divisible by 97. Yes, 194 is divisible by 97 (97 × 2 = 194).
Problem 4
Can 2912 be divisible by 97 following the divisibility rule?
Yes, 2912 is divisible by 97.
Explanation
To see if 2912 is divisible by 97, follow these steps:
1) Multiply the last digit by 29, 2 × 29 = 58.
2) Subtract the result from the remaining digits excluding the last digit, 291 - 58 = 233.
3) Check if 233 is divisible by 97. Yes, 233 is divisible by 97 (97 × 2 + 39, check reveals a mistake in initial calculation, confirming it's not divisible).
Problem 5
Check the divisibility rule of 97 for 9703.
No, 9703 is not divisible by 97.
Explanation
To check if 9703 is divisible by 97, apply the rule:
1) Multiply the last digit by 29, 3 × 29 = 87.
2) Subtract the result from the remaining digits, excluding the last digit, 970 - 87 = 883.
3) Check if 883 is divisible by 97. No, 883 is not divisible by 97.
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FAQs on Divisibility Rule of 97
1.What is the divisibility rule for 97?
2.How many numbers are there between 1 and 1000 that are divisible by 97?
3.Is 194 divisible by 97?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 97 apply to all the integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 97?
7.What are some fun ways kids in United States can practice Divisibility Rule of 97 with numbers?
8.What role do numbers and Divisibility Rule of 97 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 97 skills?
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Important Glossaries for Divisibility Rule of 97
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 97 are 97, 194, 291, 388...
- 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.
- Division method: The process of dividing a number by another number to check for divisibility, used as a verification tool.
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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.
