Greatest Common Factor of 504 and 512

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 504, 512 i.e. 8 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 504 and 512 is 8.

GCF(504,512) = 8

GCF of 504 and 512

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

GCF of:
and

Greatest Common Factor of 504 and 512

GCF of 504 and 512 is 8

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

Prime Factorization of 512


2 512
2 256
2 128
2 64
2 32
2 16
2 8
2 4
2 2
1

Prime factors of 512 are 2. Prime factorization of 512 in exponential form is:

512 = 29

∴ So by taking common prime factors GCF of 504 and 512 is 8

Greatest Common Factor of 504 and 512 by matching factors method

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

Factors of 512

List of positive integer factors of 512 that divides 512 without a remainder.

1,2,4,8,16,32,64,128,256,512

Greatest Common Factor

We found the factors and prime factorization of 504 and 512. The biggest common factor number is the GCF number.
So the greatest common factor 504 and 512 is 8.

Also check out the Least Common Multiple of 504 and 512

Properties of GCF 504 and 512

(i) The GCF of 504 and 512 is associative

GCF of 504 and 512 = GCF of 512 and 504

Related Greatest Common Factor of 504

Related Greatest Common Factor of 512

Frequently Asked Questions on GCF of 504 and 512

1. What is the GCF of 504 and 512?

Answer: GCF of 504 and 512 is 8.

2. 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.

3. What are the Factors of 512?

Answer: Factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512. There are 10 integers that are factors of 512. The greatest factor of 512 is 512.

4. How to Find the GCF of 504 and 512?

Answer:

Greatest Common Factor of 504 and 512 = 8

Step 1: Find the prime factorization of 504

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

Step 2: Find the prime factorization of 512

512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

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

GCF = 2 x 2 x 2 = 8

Step 4: Therefore, the greatest common factor of 504 and 512 is 8