What is the Greatest Common Factor of 513 and 532?

Greatest common factor (GCF) of 513 and 532 is 19.

GCF(513,532) = 19

We will now calculate the prime factors of 513 and 532, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 513 and 532.

How to find the GCF of 513 and 532?

We will first find the prime factorization of 513 and 532. After we will calculate the factors of 513 and 532 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 532

Prime factors of 532 are 2, 7, 19. Prime factorization of 532 in exponential form is:

532 = 2² × 7¹ × 19¹

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 532

List of positive integer factors of 532 that divides 513 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 513 and 532. The biggest common factor number is the GCF number.
So the greatest common factor 513 and 532 is 19.

Also check out the Least Common Multiple of 513 and 532