Divisibility Rule of 510
2026-02-28 09:58 Diff
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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 510.

What is the Divisibility Rule of 510?

The divisibility rule for 510 is a method by which we can find out if a number is divisible by 510 or not without using the division method. Check whether 3060 is divisible by 510 using the divisibility rule.

Step 1: Check divisibility by 2, 3, and 5, since 510 = 2 × 3 × 5 × 17. 
The number should end with an even digit for divisibility by 2.
The sum of the digits should be divisible by 3.
The number should end with a 0 or 5 for divisibility by 5.

Step 2: Confirm divisibility by 17. 
Divide the number by 17 and check if the result is an integer.

Step 3: If the number passes all the above checks, it is divisible by 510.


 

Tips and Tricks for Divisibility Rule of 510

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 510.

Know the multiples of 510: Memorize multiples of 510 to quickly check divisibility. If the result from the division is an integer, then the number is divisible by 510.

Use negative numbers for verification: If the result we get after subtraction or division is negative, consider it as positive for checking the divisibility of a number.

Break it down: Since 510 is a product of several factors, check divisibility using smaller factors first (2, 3, and 5) before checking with 17.

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 verify and also learn.
 

Common Mistakes and How to Avoid Them in Divisibility Rule of 510

The divisibility rule of 510 helps us quickly check if the given number is divisible by 510, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you.
 

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Problem 1

Is 2040 divisible by 510?

Okay, lets begin

Yes, 2040 is divisible by 510.

Explanation

To determine if 2040 is divisible by 510, we will use the divisibility rules for 2, 3, 5, and 17 (since 510 = 2 × 3 × 5 × 17).

  1) Check divisibility by 2: The last digit is 0, which is even, so 2040 is divisible by 2.

  2) Check divisibility by 3: Sum of digits is 2 + 0 + 4 + 0 = 6, which is divisible by 3.

3) Check divisibility by 5: The last digit is 0, so 2040 is divisible by 5.  
4) Check divisibility by 17: Divide 2040 by 17, which gives 120, an integer.  

Since 2040 satisfies all these conditions, it is divisible by 510.

Well explained 👍

Problem 2

Check the divisibility rule of 510 for 7650.

Okay, lets begin

Yes, 7650 is divisible by 510.

Explanation

To verify if 7650 is divisible by 510, follow the divisibility rules for 2, 3, 5, and 17.  

1) Check divisibility by 2: The last digit is 0, which is even, so 7650 is divisible by 2.  

2) Check divisibility by 3: Sum of digits is 7 + 6 + 5 + 0 = 18, which is divisible by 3.

3) Check divisibility by 5: The last digit is 0, so 7650 is divisible by 5.  
4) Check divisibility by 17: Divide 7650 by 17, which gives 450, an integer.  

All conditions are satisfied, confirming that 7650 is divisible by 510.

Well explained 👍

Problem 3

Is -1530 divisible by 510?

Okay, lets begin

Yes, -1530 is divisible by 510.

Explanation

 For negative numbers, check using the same rules as positive numbers. Remove the negative sign and apply the rules.  

1) Check divisibility by 2: The last digit is 0, so 1530 is divisible by 2.  
2) Check divisibility by 3: Sum of digits is 1 + 5 + 3 + 0 = 9, which is divisible by 3.

3) Check divisibility by 5: The last digit is 0, so 1530 is divisible by 5.

4) Check divisibility by 17: Divide 1530 by 17, which gives 90, an integer.  

Thus, -1530 is divisible by 510.

Well explained 👍

Problem 4

Can 2500 be divisible by 510 following the divisibility rule?

Okay, lets begin

No, 2500 isn't divisible by 510.

Explanation

To check if 2500 is divisible by 510, apply the divisibility rules for 2, 3, 5, and 17.  

1) Check divisibility by 2: The last digit is 0, so 2500 is divisible by 2.  
2) Check divisibility by 3: Sum of digits is 2 + 5 + 0 + 0 = 7, which is not divisible by 3.  

Since 2500 fails the divisibility test for 3, it is not divisible by 510.

Well explained 👍

Problem 5

Check the divisibility rule of 510 for 8670.

Okay, lets begin

Yes, 8670 is divisible by 510.
 

Explanation

To check the divisibility of 8670 by 510, apply the rules for 2, 3, 5, and 17.  
1) Check divisibility by 2: The last digit is 0, so 8670 is divisible by 2.  

2) Check divisibility by 3: Sum of digits is 8 + 6 + 7 + 0 = 21, which is divisible by 3.

  3) Check divisibility by 5: The last digit is 0, so 8670 is divisible by 5.  

4) Check divisibility by 17: Divide 8670 by 17, which gives 510, an integer.  

As all conditions are satisfied, 8670 is divisible by 510.

Well explained 👍

FAQs on Divisibility Rule of 510

1.What is the divisibility rule for 510?

The divisibility rule for 510 involves checking divisibility by 2, 3, and 5, and finally confirming divisibility by 17.

2.How many numbers are there between 1 and 1000 that are divisible by 510?

There are 1 number that can be divided by 510 between 1 and 1000. The number is - 510.
 

3.Is 1020 divisible by 510?

Yes, because 1020 is a multiple of 510 (510 × 2 = 1020).

4.What if I get 0 after division?

If you get 0 as a remainder after division, it is considered as the number is divisible by 510.
Does the divisibility rule of 510 apply to all integers?

5. Does the divisibility rule of 510 apply to all integers?

Yes, the divisibility rule of 510 applies to all integers.

Important Glossary for Divisibility Rule of 510

  • 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 510 are 510, 1020, 1530, etc.
  • Factors: Numbers that evenly divide another number. For 510, factors include 2, 3, 5, and 17.
  • Integer: Whole numbers that include positive, negative numbers, and zero.
  • Verification: The process of confirming the accuracy of a calculation or result, often by using a different method.
     

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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.