Divisibility Rule of 71
2026-02-28 08:43 Diff
https://brightchamps.com/en-us/math/numbers/divisibility-rule-of-71

388 Learners

Last updated on August 5, 2025

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.

Explore Our Programs

Download Worksheets

Problem 1

Is 5680 divisible by 71?

Okay, lets begin

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.

Well explained 👍

Problem 2

Check the divisibility rule of 71 for 4977.

Okay, lets begin

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).
 

Well explained 👍

Problem 3

Is -2131 divisible by 71?

Okay, lets begin

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.

Well explained 👍

Problem 4

Can 852 be divisible by 71 following the divisibility rule?

Okay, lets begin

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.

Well explained 👍

Problem 5

Check the divisibility rule of 71 for 6397.

Okay, lets begin

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).

Well explained 👍

FAQs on Divisibility Rule of 71

1.What is the divisibility rule for 71?

The divisibility rule for 71 involves doubling the last digit, subtracting the result from the remaining digits excluding the last digit, and then checking if the result is a multiple of 71.

2.How many numbers are there between 1 and 1000 that are divisible by 71?

There are 14 numbers that can be divided by 71 between 1 and 1000. The numbers are 71, 142, 213, 284, 355, 426, 497, 568, 639, 710, 781, 852, 923, 994.

3.Is 142 divisible by 71?

Yes, because 142 is a multiple of 71 (71 × 2 = 142).

4.What if I get 0 after subtracting?

If you get 0 after subtracting, the number is considered divisible by 71.

5.Does the divisibility rule of 71 apply to all integers?

Yes, the divisibility rule of 71 applies to all integers.

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.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.