Divisibility Rule of 505
2026-02-28 10:33 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 things. In this topic, we will learn about the divisibility rule of 505.

What is the Divisibility Rule of 505?

The divisibility rule for 505 is a method by which we can find out if a number is divisible by 505 or not without using the division method. Check whether 1515 is divisible by 505 with the divisibility rule.

Step 1: Check if the number is divisible by 5. Since 1515 ends in 5, it is divisible by 5.

Step 2: Check if the number is divisible by 101. Divide 1515 by 101 to see if it results in an integer. \(1515 \div 101 = 15\), which is an integer.

Step 3: Since 1515 is divisible by both 5 and 101, it is divisible by 505.

Tips and Tricks for Divisibility Rule of 505

Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 505.

Know the factors of 505: Memorize the factors of 505 (5 and 101) to quickly check the divisibility. If a number is divisible by both 5 and 101, then it is divisible by 505.

Use mental math: Quickly identify if a number can be divided by 5 by checking the last digit. Use division for small numbers to verify divisibility by 101.

Repeat the process for large numbers:  Students should keep repeating the divisibility process with the factors (5 and 101) until they confirm divisibility by both.

For example: Check if 2525 is divisible by 505 using the divisibility test.  
2525 ends in 5, so it is divisible by 5.  
Next, divide 2525 by 101, \(2525 \div 101 = 25\), which is an integer.  
Since 2525 is divisible by both 5 and 101, it is divisible by 505.

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 D

The divisibility rule of 505 helps us quickly check if a given number is divisible by 505, but common mistakes can lead to incorrect calculations. Here we will understand some common mistakes and how to avoid them.
 

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Problem 1

Is 5050 divisible by 505?

Okay, lets begin

Yes, 5050 is divisible by 505.
 

Explanation

To check if 5050 is divisible by 505, we can use the divisibility rule:

1) Check if the last three digits form a number divisible by 505. Here, the last three digits are 050.

2) Since 050 is actually 50, we see that 50 is not divisible by 505.

3) However, the number 5050 is 505 times 10 (505 x 10 = 5050), thus it is divisible by 505.

Well explained 👍

Problem 2

Check the divisibility rule of 505 for 1010.

Okay, lets begin

No, 1010 is not divisible by 505.

Explanation

 To check if 1010 is divisible by 505, we follow these steps:

1) Check if the last three digits form a number divisible by 505. Here, the last three digits are 010.

2) Since 010 is actually 10, and 10 is not divisible by 505, 1010 is not divisible by 505.

Well explained 👍

Problem 3

Is -2020 divisible by 505?

Okay, lets begin

No, -2020 is not divisible by 505.

Explanation

 To check if -2020 is divisible by 505, we follow these steps:

1) Ignore the negative sign and consider the absolute value, which is 2020.

2) Check if the last three digits form a number divisible by 505. Here, the last three digits are 020.

3) Since 020 is actually 20, and 20 is not divisible by 505, 2020 is not divisible by 505.

Well explained 👍

Problem 4

Can 50500 be divisible by 505 following the divisibility rule?

Okay, lets begin

Yes, 50500 is divisible by 505.
 

Explanation

To check if 50500 is divisible by 505, we follow these steps:

1) Check if the last three digits form a number divisible by 505. Here, the last three digits are 500.

2) Since 500 is not divisible by 505, but because 50500 is 505 times 100 (505 x 100 = 50500), it is divisible by 505.

Well explained 👍

Problem 5

Check the divisibility rule of 505 for 2525.

Okay, lets begin

No, 2525 is not divisible by 505.

Explanation

 To check if 2525 is divisible by 505, we follow these steps:

1) Check if the last three digits form a number divisible by 505. Here, the last three digits are 525.

2) Since 525 is not divisible by 505, 2525 is not divisible by 505.

Well explained 👍

FAQs on Divisibility Rule of 505

1.What is the divisibility rule for 505?

The divisibility rule for 505 requires checking if a number is divisible by both 5 and 101.
 

2.How many numbers are there between 1 and 1000 that are divisible by 505?

There are 1 number that can be divided by 505 between 1 and 1000. The number is 505.
 

3.Is 2020 divisible by 505?

No, because 2020 is not divisible by 101.

4.What if I get a non-integer result after division?

 If you get a non-integer result after division, the number is not divisible by 505.
 

5.Does the divisibility rule of 505 apply to all integers?

Yes, the divisibility rule of 505 applies to all integers.

Important Glossaries for Divisibility Rule of 505

  • Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 5 if the number ends with 0 or 5.
  • Factors: Numbers that divide another number without leaving a remainder. For example, the factors of 505 are 5 and 101.
  • Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
  • Division: The process of dividing one number by another.
  • Verification: The process of confirming the correctness of a calculation or result, often by using an alternative 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.