Greatest Common Factor of 500 and 505

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 500, 505 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 500 and 505 is 5.

GCF(500,505) = 5

GCF of 500 and 505

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 500 and 505

GCF of 500 and 505 is 5

Prime Factorization of 500


2 500
2 250
5 125
5 25
5 5
1

Prime factors of 500 are 2,5. Prime factorization of 500 in exponential form is:

500 = 22×53

Prime Factorization of 505


5 505
101 101
1

Prime factors of 505 are 5,101. Prime factorization of 505 in exponential form is:

505 = 51×1011

∴ So by taking common prime factors GCF of 500 and 505 is 5

Greatest Common Factor of 500 and 505 by matching factors method

Factors of 500

List of positive integer factors of 500 that divides 500 without a remainder.

1,2,4,5,10,20,25,50,100,125,250,500

Factors of 505

List of positive integer factors of 505 that divides 505 without a remainder.

1,5,101,505

Greatest Common Factor

We found the factors and prime factorization of 500 and 505. The biggest common factor number is the GCF number.
So the greatest common factor 500 and 505 is 5.

Also check out the Least Common Multiple of 500 and 505

Properties of GCF 500 and 505

(i) The GCF of 500 and 505 is associative

GCF of 500 and 505 = GCF of 505 and 500

Related Greatest Common Factor of 500

Related Greatest Common Factor of 505

Frequently Asked Questions on GCF of 500 and 505

1. What is the GCF of 500 and 505?

Answer: GCF of 500 and 505 is 5.

2. What are the Factors of 500?

Answer: Factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500. There are 12 integers that are factors of 500. The greatest factor of 500 is 500.

3. What are the Factors of 505?

Answer: Factors of 505 are 1, 5, 101, 505. There are 4 integers that are factors of 505. The greatest factor of 505 is 505.

4. How to Find the GCF of 500 and 505?

Answer:

Greatest Common Factor of 500 and 505 = 5

Step 1: Find the prime factorization of 500

500 = 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 505

505 = 5 x 101

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 5

Step 4: Therefore, the greatest common factor of 500 and 505 is 5