What is the Greatest Common Factor of 500 and 516?

Greatest common factor (GCF) of 500 and 516 is 4.

GCF(500,516) = 4

We will now calculate the prime factors of 500 and 516, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 500 and 516.

How to find the GCF of 500 and 516?

We will first find the prime factorization of 500 and 516. After we will calculate the factors of 500 and 516 and find the biggest common factor number .

Step-1: Prime Factorization of 500

Prime factors of 500 are 2, 5. Prime factorization of 500 in exponential form is:

500 = 2² × 5³

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 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

Step-4: Factors of 516

List of positive integer factors of 516 that divides 500 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 500 and 516. The biggest common factor number is the GCF number.
So the greatest common factor 500 and 516 is 4.

Also check out the Least Common Multiple of 500 and 516