Divisibility Rule of 509
2026-02-28 11:31 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 509.

What is the Divisibility Rule of 509?


The divisibility rule for 509 is a method by which we can find out if a number is divisible by 509 or not without using the division method. Check whether 1018 is divisible by 509 with the divisibility rule.

Step 1: Since 509 is a relatively large number, the simplest method is to directly check divisibility by performing the division or by recognizing if the number is a multiple of 509 through memorization or calculation.

Step 2: If you know the multiples of 509, check if 1018 matches any of those multiples. In this case, 1018 is 509 × 2.

Step 3: As 1018 is a multiple of 509, therefore, the number is divisible by 509.


 

Tips and Tricks for Divisibility Rule of 509

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 509.

Know the multiples of 509: Memorize the multiples of 509 (509, 1018, 1527, 2036…etc.) to quickly check the divisibility. If the number matches a multiple of 509, then it is divisible by 509.

Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.

Common Mistakes and How to Avoid Them in Divisibility Rule of 509

The divisibility rule of 509 helps us quickly check if the given number is divisible by 509, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes that will help you to avoid them.
 

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Problem 1

Is 1018 divisible by 509?

Okay, lets begin

Yes, 1018 is divisible by 509.

Explanation

To verify if 1018 is divisible by 509, consider the following steps:

1) Double the last digit of the number: 8 × 2 = 16.

  2) Subtract the result from the remaining digits, excluding the last digit: 101 - 16 = 85. 

3) Check if the result is a multiple of 509. No, 85 is not a multiple of 509, but we miscalculated the subtraction. Let's verify directly instead: 1018 ÷ 509 = 2, which means 1018 is divisible by 509.

Well explained 👍

Problem 2

Check the divisibility rule of 509 for 2545.

Okay, lets begin

No, 2545 is not divisible by 509. 

Explanation

To check if 2545 is divisible by 509, use these steps:

  1) Double the last digit of the number: 5 × 2 = 10.

2) Subtract the result from the remaining digits, excluding the last digit: 254 - 10 = 244.  

3) Check if 244 is a multiple of 509. No, 244 is not a multiple of 509, hence 2545 is not divisible by 509.

Well explained 👍

Problem 3

Is -1527 divisible by 509?

Okay, lets begin

Yes, -1527 is divisible by 509. 

Explanation

To determine if -1527 is divisible by 509, follow these steps (ignoring the negative sign):  
1) Double the last digit of the number: 7 x 2 = 14.  
2) Subtract the result from the remaining digits, excluding the last digit: 152 - 14 = 138.  
3) Check if 138 is a multiple of 509. No, but direct division shows 1527÷ 509 = 3, which confirms divisibility.

Well explained 👍

Problem 4

Can 3054 be divisible by 509 following the divisibility rule?

Okay, lets begin

Yes, 3054 is divisible by 509. 

Explanation

To verify if 3054 is divisible by 509, follow these steps:  

1) Double the last digit of the number: 4 × 2 = 8.  

2) Subtract the result from the remaining digits, excluding the last digit: 305 - 8 = 297.  

3) Check if 297 is a multiple of 509. No, but direct division 3054÷509 = 6 confirms divisibility.

Well explained 👍

Problem 5

Check the divisibility rule of 509 for 4072.

Okay, lets begin

 No, 4072 is not divisible by 509.  
 

Explanation

To check the divisibility of 4072 by 509, follow these steps:  

1) Double the last digit of the number: 2 x 2 = 4.

  2) Subtract the result from the remaining digits, excluding the last digit: 407 - 4 = 403.  

3) Check if 403 is a multiple of 509. No, 403 is not a multiple of 509, hence 4072 is not divisible by 509.

Well explained 👍

FAQs on Divisibility Rule of 509

1.What is the divisibility rule for 509?

The divisibility rule for 509 involves recognizing its multiples or performing division to verify.
 

2. How many numbers are there between 1 and 2000 that are divisible by 509?

There are 3 numbers that can be divided by 509 between 1 and 2000. The numbers are 509, 1018, and 1527.

3.Is 1527 divisible by 509?

Yes, because 1527 is a multiple of 509 (509 × 3 = 1527)

4.What if I get 0 after performing division?

If you get 0 as a remainder, it means the number is divisible by 509.
 

5.Does the divisibility rule of 509 apply to all integers?

Yes, the divisibility rule of 509 applies to all integers.

Important Glossaries for Divisibility Rule of 509

  • Divisibility rule: The set of guidelines used to determine if a number is divisible by another number.
  • Multiples: The results obtained by multiplying a number by an integer. For example, multiples of 509 are 509, 1018, 1527, etc.
  • Integer: A whole number that can be positive, negative, or zero.
  • Division: A mathematical process of determining how many times one number is contained within another.
  • Verification: The process of checking calculations to ensure correctness.
     

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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.