What is the Greatest Common Factor of 498 and 513?

Greatest common factor (GCF) of 498 and 513 is 3.

GCF(498,513) = 3

We will now calculate the prime factors of 498 and 513, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 498 and 513.

How to find the GCF of 498 and 513?

We will first find the prime factorization of 498 and 513. After we will calculate the factors of 498 and 513 and find the biggest common factor number .

Step-1: Prime Factorization of 498

Prime factors of 498 are 2, 3, 83. Prime factorization of 498 in exponential form is:

498 = 2¹ × 3¹ × 83¹

Step-2: Prime Factorization of 513

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

513 = 3³ × 19¹

Step-3: Factors of 498

List of positive integer factors of 498 that divides 498 without a remainder.

1, 2, 3, 6, 83, 166, 249

Step-4: Factors of 513

List of positive integer factors of 513 that divides 498 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 498 and 513. The biggest common factor number is the GCF number.
So the greatest common factor 498 and 513 is 3.

Also check out the Least Common Multiple of 498 and 513