What is the Greatest Common Factor of 500 and 514?

Greatest common factor (GCF) of 500 and 514 is 2.

GCF(500,514) = 2

We will now calculate the prime factors of 500 and 514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 500 and 514.

How to find the GCF of 500 and 514?

We will first find the prime factorization of 500 and 514. After we will calculate the factors of 500 and 514 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 514

Prime factors of 514 are 2, 257. Prime factorization of 514 in exponential form is:

514 = 2¹ × 257¹

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 514

List of positive integer factors of 514 that divides 500 without a remainder.

1, 2, 257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 500 and 514. The biggest common factor number is the GCF number.
So the greatest common factor 500 and 514 is 2.

Also check out the Least Common Multiple of 500 and 514