What is the Greatest Common Factor of 514 and 520?

Greatest common factor (GCF) of 514 and 520 is 2.

GCF(514,520) = 2

We will now calculate the prime factors of 514 and 520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 514 and 520.

How to find the GCF of 514 and 520?

We will first find the prime factorization of 514 and 520. After we will calculate the factors of 514 and 520 and find the biggest common factor number .

Step-1: Prime Factorization of 514

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

514 = 2¹ × 257¹

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 514

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

1, 2, 257

Step-4: Factors of 520

List of positive integer factors of 520 that divides 514 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 514 and 520. The biggest common factor number is the GCF number.
So the greatest common factor 514 and 520 is 2.

Also check out the Least Common Multiple of 514 and 520