What is the Greatest Common Factor of 507 and 516?

Greatest common factor (GCF) of 507 and 516 is 3.

GCF(507,516) = 3

We will now calculate the prime factors of 507 and 516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 507 and 516.

How to find the GCF of 507 and 516?

We will first find the prime factorization of 507 and 516. After we will calculate the factors of 507 and 516 and find the biggest common factor number .

Step-1: Prime Factorization of 507

Prime factors of 507 are 3, 13. Prime factorization of 507 in exponential form is:

507 = 3¹ × 13²

Step-2: Prime Factorization of 516

Prime factors of 516 are 2, 3, 43. Prime factorization of 516 in exponential form is:

516 = 2² × 3¹ × 43¹

Step-3: Factors of 507

List of positive integer factors of 507 that divides 507 without a remainder.

1, 3, 13, 39, 169

Step-4: Factors of 516

List of positive integer factors of 516 that divides 507 without a remainder.

1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 507 and 516. The biggest common factor number is the GCF number.
So the greatest common factor 507 and 516 is 3.

Also check out the Least Common Multiple of 507 and 516