What is the Greatest Common Factor of 513 and 519?

Greatest common factor (GCF) of 513 and 519 is 3.

GCF(513,519) = 3

We will now calculate the prime factors of 513 and 519, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 513 and 519.

How to find the GCF of 513 and 519?

We will first find the prime factorization of 513 and 519. After we will calculate the factors of 513 and 519 and find the biggest common factor number .

Step-1: Prime Factorization of 513

Prime factors of 513 are 3, 19. Prime factorization of 513 in exponential form is:

513 = 3³ × 19¹

Step-2: Prime Factorization of 519

Prime factors of 519 are 3, 173. Prime factorization of 519 in exponential form is:

519 = 3¹ × 173¹

Step-3: Factors of 513

List of positive integer factors of 513 that divides 513 without a remainder.

1, 3, 9, 19, 27, 57, 171

Step-4: Factors of 519

List of positive integer factors of 519 that divides 513 without a remainder.

1, 3, 173

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 513 and 519. The biggest common factor number is the GCF number.
So the greatest common factor 513 and 519 is 3.

Also check out the Least Common Multiple of 513 and 519