What is the Greatest Common Factor of 500 and 508?

Greatest common factor (GCF) of 500 and 508 is 4.

GCF(500,508) = 4

We will now calculate the prime factors of 500 and 508, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 500 and 508.

How to find the GCF of 500 and 508?

We will first find the prime factorization of 500 and 508. After we will calculate the factors of 500 and 508 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 508

Prime factors of 508 are 2, 127. Prime factorization of 508 in exponential form is:

508 = 2² × 127¹

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 508

List of positive integer factors of 508 that divides 500 without a remainder.

1, 2, 4, 127, 254

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 500 and 508. The biggest common factor number is the GCF number.
So the greatest common factor 500 and 508 is 4.

Also check out the Least Common Multiple of 500 and 508