Greatest Common Factor of 500 and 504

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, 504 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 500 and 504 is 4.

GCF(500,504) = 4

GCF of 500 and 504

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

GCF of:
and

Greatest Common Factor of 500 and 504

GCF of 500 and 504 is 4

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 504


2 504
2 252
2 126
3 63
3 21
7 7
1

Prime factors of 504 are 2,3,7. Prime factorization of 504 in exponential form is:

504 = 23×32×71

∴ So by taking common prime factors GCF of 500 and 504 is 4

Greatest Common Factor of 500 and 504 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 504

List of positive integer factors of 504 that divides 504 without a remainder.

1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504

Greatest Common Factor

We found the factors and prime factorization of 500 and 504. The biggest common factor number is the GCF number.
So the greatest common factor 500 and 504 is 4.

Also check out the Least Common Multiple of 500 and 504

Properties of GCF 500 and 504

(i) The GCF of 500 and 504 is associative

GCF of 500 and 504 = GCF of 504 and 500

Related Greatest Common Factor of 500

Related Greatest Common Factor of 504

Frequently Asked Questions on GCF of 500 and 504

1. What is the GCF of 500 and 504?

Answer: GCF of 500 and 504 is 4.

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 504?

Answer: Factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. There are 24 integers that are factors of 504. The greatest factor of 504 is 504.

4. How to Find the GCF of 500 and 504?

Answer:

Greatest Common Factor of 500 and 504 = 4

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 504

504 = 2 x 2 x 2 x 3 x 3 x 7

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

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 500 and 504 is 4