Divisibility Rule of 710
2026-02-28 08:21 Diff
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Last updated on August 5, 2025

The divisibility rule is a way to determine 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 items. In this topic, we will learn about the divisibility rule of 710.

What is the Divisibility Rule of 710?

The divisibility rule for 710 is a method by which we can determine if a number is divisible by 710 without using the division method. Let's check whether 4260 is divisible by 710 using the divisibility rule.

Step 1: Check if the number is divisible by both 71 and 10. Since 710 is the product of 71 and 10, a number is divisible by 710 if it meets the criteria for both.

Step 2: To check divisibility by 71, use a variation of the rule for 7. For simplicity, let's say the rule involves subtracting twice the last digit from the rest of the number. In 4260, the last digit is 0, so the rule simplifies as 426 - (0 × 2) = 426. Since checking divisibility by 71 is complex, using a calculator or known divisibility method is preferred.

Step 3: For divisibility by 10, the number must end in 0. Since 4260 ends in 0, it meets this criterion.

Since 4260 is divisible by 71 and 10, it is divisible by 710.

Tips and Tricks for Divisibility Rule of 710

Know the multiples of 710: Memorize the multiples of 710 (710, 1420, 2130, etc.) to quickly check divisibility. If the number is a multiple of 710, it is divisible by 710.

Use divisibility tests for 71 and 10:

For smaller calculations, ensure the number meets divisibility for both 71 and 10.

Repeat the process for large numbers:

If the number is large, break it down and repeatedly check divisibility until you get a manageable number.

Use the division method to verify:

Use long division to verify your result for accuracy.

Common Mistakes and How to Avoid Them in Divisibility Rule of 710

The divisibility rule of 710 helps us quickly check if a number is divisible by 710, but common mistakes can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
 

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Problem 1

Is 4260 divisible by 710?

Okay, lets begin

No, 4260 is not divisible by 710.
 

Explanation

To determine if 4260 is divisible by 710, check the divisibility by 71 and 10 separately. 
1) For 71, consider the last digit 0, remove it, and check if 426 is divisible by 71. 426 ÷ 71 = 6 (remainder 0), so 426 is divisible by 71.
2) For 10, check if the last digit is 0. Yes, 4260 ends in 0, so it is divisible by 10.
3) Since 426 is divisible by 71 and 4260 is divisible by 10, it is also divisible by 710. However, since the initial division was incorrect, 4260 is not divisible by 710.

Well explained 👍

Problem 2

Verify if 1420 can be divided by 710.

Okay, lets begin

Yes, 1420 is divisible by 710.
 

Explanation

To verify if 1420 is divisible by 710, use the criteria for 71 and 10. 
1) Check divisibility by 71: Consider the last digit 0, remove it to get 142. 142 ÷ 71 = 2 (remainder 0), so 142 is divisible by 71.
2) Check divisibility by 10: The number 1420 ends in 0, so it is divisible by 10.
3) Since 142 is divisible by 71 and 1420 is divisible by 10, 1420 is divisible by 710.

Well explained 👍

Problem 3

Determine if 2130 is divisible by 710.

Okay, lets begin

No, 2130 is not divisible by 710.

Explanation

To determine if 2130 is divisible by 710, check the divisibility by 71 and 10. 
1) Check divisibility by 71: Consider the last digit 0, remove it to get 213. 213 ÷ 71 = 3 (remainder 0), so 213 is divisible by 71.
2) Check divisibility by 10: The number 2130 ends in 0, so it is divisible by 10.
3) Although 213 is divisible by 71, 2130 is not divisible by 710 because 213 was incorrectly calculated as divisible by 71.
 

Well explained 👍

Problem 4

Can 4970 be divisible by 710?

Okay, lets begin

No, 4970 is not divisible by 710.

Explanation

To check if 4970 is divisible by 710, evaluate divisibility by 71 and 10.
1) Check divisibility by 71: Consider the last digit 0, remove it to get 497. 497 ÷ 71 = 7 (remainder 0), so 497 is divisible by 71.
2) Check divisibility by 10: The number 4970 ends in 0, so it is divisible by 10.
3) Since the initial assumption was incorrect, 4970 is not divisible by 710.
 

Well explained 👍

Problem 5

Verify if 7100 can be divided by 710.

Okay, lets begin

Yes, 7100 is divisible by 710.
 

Explanation

To verify if 7100 is divisible by 710, use divisibility rules for 71 and 10.
1) Check divisibility by 71: Consider the last digit 0, remove it to get 710. 710 ÷ 71 = 10 (remainder 0), so 710 is divisible by 71.
2) Check divisibility by 10: The number 7100 ends in 0, so it is divisible by 10.
3) Since 710 is divisible by 71 and 7100 is divisible by 10, 7100 is divisible by 710.

Well explained 👍

FAQs on Divisibility Rule of 710

1.What is the divisibility rule for 710?

A number is divisible by 710 if it is divisible by both 71 and 10.
 

2.How many numbers between 1 and 5000 are divisible by 710?

There are 7 numbers divisible by 710 between 1 and 5000. These are 710, 1420, 2130, 2840, 3550, 4260, and 4970.
 

3.Is 2840 divisible by 710?

Yes, because 2840 is a multiple of 710 (710 × 4 = 2840).

4.What if I get 0 after subtraction?

If you meet the divisibility conditions for both 71 and 10, a 0 result in subtraction confirms divisibility by 71.

5.Does the divisibility rule of 710 apply to all integers?

Yes, the divisibility rule of 710 applies to all integers.
 

Important Glossaries for Divisibility Rule of 710

  • Divisibility Rule: The set of rules used to determine whether a number is divisible by another number.
  • Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 710 are 710, 1420, 2130, etc.
  • Integer: Numbers that include all whole numbers, negative numbers, and zero.
  • Product: The result of multiplying two numbers together. For example, 710 is the product of 71 and 10.
  • Subtraction: The process of finding the difference between two numbers by reducing one from another.

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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.