What is the Greatest Common Factor of 513 and 522?

Greatest common factor (GCF) of 513 and 522 is 9.

GCF(513,522) = 9

We will now calculate the prime factors of 513 and 522, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 513 and 522.

How to find the GCF of 513 and 522?

We will first find the prime factorization of 513 and 522. After we will calculate the factors of 513 and 522 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 522

Prime factors of 522 are 2, 3, 29. Prime factorization of 522 in exponential form is:

522 = 2¹ × 3² × 29¹

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 522

List of positive integer factors of 522 that divides 513 without a remainder.

1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 513 and 522. The biggest common factor number is the GCF number.
So the greatest common factor 513 and 522 is 9.

Also check out the Least Common Multiple of 513 and 522