What is the Greatest Common Factor of 504 and 518?

Greatest common factor (GCF) of 504 and 518 is 14.

GCF(504,518) = 14

We will now calculate the prime factors of 504 and 518, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 504 and 518.

How to find the GCF of 504 and 518?

We will first find the prime factorization of 504 and 518. After we will calculate the factors of 504 and 518 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 518

Prime factors of 518 are 2, 7, 37. Prime factorization of 518 in exponential form is:

518 = 2¹ × 7¹ × 37¹

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 518

List of positive integer factors of 518 that divides 504 without a remainder.

1, 2, 7, 14, 37, 74, 259

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 504 and 518. The biggest common factor number is the GCF number.
So the greatest common factor 504 and 518 is 14.

Also check out the Least Common Multiple of 504 and 518