What is the Greatest Common Factor of 504 and 512?

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

GCF(504,512) = 8

We will now calculate the prime factors of 504 and 512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 504 and 512.

How to find the GCF of 504 and 512?

We will first find the prime factorization of 504 and 512. After we will calculate the factors of 504 and 512 and find the biggest common factor number .

Step-1: Prime Factorization of 504

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

504 = 2³ × 3² × 7¹

Step-2: Prime Factorization of 512

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

512 = 2⁹

Step-3: 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

Step-4: Factors of 512

List of positive integer factors of 512 that divides 504 without a remainder.

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

Final Step: Biggest Common Factor Number

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