What is the Greatest Common Factor of 500 and 520?

Greatest common factor (GCF) of 500 and 520 is 20.

GCF(500,520) = 20

We will now calculate the prime factors of 500 and 520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 500 and 520.

How to find the GCF of 500 and 520?

We will first find the prime factorization of 500 and 520. After we will calculate the factors of 500 and 520 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 520

Prime factors of 520 are 2, 5, 13. Prime factorization of 520 in exponential form is:

520 = 2³ × 5¹ × 13¹

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 520

List of positive integer factors of 520 that divides 500 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 500 and 520. The biggest common factor number is the GCF number.
So the greatest common factor 500 and 520 is 20.

Also check out the Least Common Multiple of 500 and 520