200 LearnersLast updated on May 26th, 2025
Divisibility Rule of 91
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 91.
What is the Divisibility Rule of 91?
The divisibility rule for 91 is a method by which we can find out if a number is divisible by 91 or not without using the division method. Check whether 728 is divisible by 91 with the divisibility rule.
Step 1: Check if the number is divisible by both 7 and 13, as 91 is the product of these two prime numbers (7 × 13).
Step 2: Use the divisibility rule for 7 first. Multiply the last digit by 2, here in 728, 8 is the last digit, multiply it by 2. 8 × 2 = 16.
Step 3: Subtract the result from Step 2 from the remaining values but do not include the last digit. i.e., 72–16 = 56.
Step 4: 56 is a multiple of 7, so 728 is divisible by 7.
Step 5: Now, check divisibility by 13. Double the last digit and add it to the rest of the number. 8 × 2 = 16, and 72 + 16 = 88.
Step 6: 88 is a multiple of 13, so 728 is also divisible by 13.
Since 728 is divisible by both 7 and 13, it is divisible by 91.
Tips and Tricks for Divisibility Rule of 91
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 91.
- Know the multiples of 91: Memorize the multiples of 91 (91, 182, 273, 364, etc.) to quickly check divisibility. If the result of the checks is divisible by both 7 and 13, then the number is divisible by 91.
- Use the breakdown method: If a number is large, break it down into smaller parts and check each part's divisibility by 7 and 13.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by both 7 and 13.
For example: Check if 1820 is divisible by 91 using the divisibility test. First, check divisibility by 7: Multiply the last digit by 2, i.e., 0 × 2 = 0. Subtract 0 from the remaining digits, 182–0 = 182.
Check 182: Multiply the last digit by 2, 2 × 2 = 4. Subtract from the remaining digits, 18–4 = 14.14 is a multiple of 7, so 1820 is divisible by 7.
Now, check divisibility by 13: Double the last digit and add it to the rest of the number, 0 × 2 = 0, and 182 + 0 = 182. 182 is a multiple of 13, so 1820 is divisible by 13. Since 1820 is divisible by both 7 and 13, it is divisible by 91.
- 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 91
The divisibility rule of 91 helps us to quickly check if the given number is divisible by 91, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps for both 7 and 13.
Students should follow the correct steps for divisibility by 7 and 13, ensuring both checks are satisfied.
Divisibility Rule of 91 Examples
Problem 1
Is the number 3640 divisible by 91?
Yes, 3640 is divisible by 91.
Explanation
For checking the divisibility of 3640 by 91, follow these steps:
1) Divide 3640 by 91 to see if it results in a whole number.
2) \(3640 \div 91 = 40\).
3) Since the result is a whole number, 3640 is divisible by 91.
Problem 2
Can we determine if 819 is divisible by 91 using a special method?
No, 819 is not divisible by 91.
Explanation
To check if 819 is divisible by 91, perform the division:
1) Divide 819 by 91 to check for a whole number.
2) \(819 \div 91 \approx 9.010989\).
3) Since the result is not a whole number, 819 is not divisible by 91.
Problem 3
Is the negative number -182 divisible by 91?
Yes, -182 is divisible by 91.
Explanation
To check if -182 is divisible by 91, first remove the negative sign and check divisibility:
1) Divide 182 by 91.
2) \(182 \div 91 = 2\).
3) Since the result is a whole number, -182 is divisible by 91.
Problem 4
Check if 273 is divisible by 91.
No, 273 is not divisible by 91.
Explanation
Perform the division to determine if 273 is divisible by 91:
1) Divide 273 by 91.
2) \(273 \div 91 \approx 3\).
3) The result is a whole number, but verify through multiplication: \(91 \times 3 = 273\). Therefore, 273 is indeed divisible by 91.
Problem 5
Is 728 divisible by 91?
Yes, 728 is divisible by 91.
Explanation
To check if 728 is divisible by 91, proceed with the division:
1) Divide 728 by 91.
2) \(728 \div 91 = 8\).
3) Since the result is a whole number, 728 is divisible by 91.
FAQs on Divisibility Rule of 91
1.What is the divisibility rule for 91?
2.How many numbers are there between 1 and 1000 that are divisible by 91?
3.Is 364 divisible by 91?
4.What if I get 0 after applying the rule?
5.Does the divisibility rule of 91 apply to all integers?
6.How can children in Indonesia use numbers in everyday life to understand Divisibility Rule of 91?
7.What are some fun ways kids in Indonesia can practice Divisibility Rule of 91 with numbers?
8.What role do numbers and Divisibility Rule of 91 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Divisibility Rule of 91 skills?
Important Glossaries for Divisibility Rule of 91
- 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 91 are 91, 182, 273, 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.
- Prime numbers: Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. For example, 7 and 13 are prime factors of 91.
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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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