146 LearnersLast updated on May 26th, 2025
Divisibility Rule of 71
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 71.
What is the Divisibility Rule of 71?
The divisibility rule for 71 is a method by which we can find out if a number is divisible by 71 or not without using the division method. Check whether 4977 is divisible by 71 with the divisibility rule.
Step 1: Double the last digit of the number, here in 4977, 7 is the last digit, so double it. 7 × 2 = 14.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 497–14 = 483.
Step 3: As it is shown that 483 is not a multiple of 71, continue the process: double the last digit of 483, which is 3, so 3 × 2 = 6. Subtract 6 from the remaining part, 48–6 = 42.
Step 4: Since 42 is not a multiple of 71, 4977 is not divisible by 71. If the result from the steps becomes a multiple of 71, then the number is divisible by 71.
Tips and Tricks for Divisibility Rule of 71
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 71.
- Know the multiples of 71: Memorize the multiples of 71 (71, 142, 213, 284…etc.) to quickly check the divisibility. The result from the subtraction should be a multiple of 71 for the number to be divisible by 71.
- Use 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 71.
For example, check if 5681 is divisible by 71 using the divisibility test. Double the last digit, 1 × 2 = 2. Subtract the remaining digits excluding the last digit by 2, 568–2 = 566.
Since 566 is a large number, continue the process: double the last digit of 566, 6 × 2 = 12. Subtract 12 from the remaining numbers excluding the last digit, 56–12 = 44.
Since 44 is not a multiple of 71, 5681 is not divisible by 71.
- 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 71
The divisibility rule of 71 helps us quickly check if the given number is divisible by 71, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes to help you avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which involve doubling the last digit and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 71.
Divisibility Rule of 71 Examples
Problem 1
Is 5680 divisible by 71?
No, 5680 is not divisible by 71.
Explanation
To check if 5680 is divisible by 71, we follow these steps:
1) Multiply the last two digits of the number by 7, 80 × 7 = 560.
2) Subtract the result from the remaining digits, excluding the last two digits, 56 – 560 = -504.
3) Check if -504 is a multiple of 71. No, -504 is not a multiple of 71.
Problem 2
Check the divisibility rule of 71 for 4977.
Yes, 4977 is divisible by 71.
Explanation
To verify if 4977 is divisible by 71, follow these steps:
1) Multiply the last two digits by 7, 77 × 7 = 539.
2) Subtract the result from the remaining digits, excluding the last two digits, 49 – 539 = -490.
3) Check if -490 is a multiple of 71. Yes, -490 is a multiple of 71 (71 × -7 = -490).
Problem 3
Is -2131 divisible by 71?
No, -2131 is not divisible by 71.
Explanation
To determine if -2131 is divisible by 71, ignore the negative sign and follow these steps:
1) Multiply the last two digits by 7, 31 × 7 = 217.
2) Subtract the result from the remaining digits, excluding the last two digits, 21 – 217 = -196.
3) Check if -196 is a multiple of 71. No, -196 is not a multiple of 71.
Problem 4
Can 852 be divisible by 71 following the divisibility rule?
No, 852 is not divisible by 71.
Explanation
To check if 852 is divisible by 71, use the rule:
1) Multiply the last two digits by 7, 52 × 7 = 364.
2) Subtract the result from the remaining digits, excluding the last two digits, 8 – 364 = -356.
3) Check if -356 is a multiple of 71. No, -356 is not a multiple of 71.
Problem 5
Check the divisibility rule of 71 for 6397.
Yes, 6397 is divisible by 71.
Explanation
To check the divisibility of 6397 by 71, follow these steps:
1) Multiply the last two digits by 7, 97 × 7 = 679.
2) Subtract the result from the remaining digits, excluding the last two digits, 63 – 679 = -616.
3) Check if -616 is a multiple of 71. Yes, -616 is a multiple of 71 (71 × -9 = -616).
FAQs on Divisibility Rule of 71
1.What is the divisibility rule for 71?
2.How many numbers are there between 1 and 1000 that are divisible by 71?
3.Is 142 divisible by 71?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 71 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 71?
7.What are some fun ways kids in United States can practice Divisibility Rule of 71 with numbers?
8.What role do numbers and Divisibility Rule of 71 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 71 skills?
Important Glossaries for Divisibility Rule of 71
- Divisibility rule: A set of steps used to find out whether a number is divisible by another number without performing division.
- Multiples: Results obtained from multiplying a number by an integer. For example, multiples of 71 are 71, 142, 213, 284, etc.
- Integers: Whole numbers, which include negative numbers, positive numbers, and zero.
- Subtraction: A process of finding the difference between two numbers by reducing one number from another.
- Positive and Negative Numbers: Positive numbers are greater than zero, while negative numbers are less than zero. In divisibility tests, negative results are treated as positive.
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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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