What is the Greatest Common Factor of 498 and 507?

Greatest common factor (GCF) of 498 and 507 is 3.

GCF(498,507) = 3

We will now calculate the prime factors of 498 and 507, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 498 and 507.

How to find the GCF of 498 and 507?

We will first find the prime factorization of 498 and 507. After we will calculate the factors of 498 and 507 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 507

Prime factors of 507 are 3, 13. Prime factorization of 507 in exponential form is:

507 = 3¹ × 13²

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 507

List of positive integer factors of 507 that divides 498 without a remainder.

1, 3, 13, 39, 169

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 498 and 507. The biggest common factor number is the GCF number.
So the greatest common factor 498 and 507 is 3.

Also check out the Least Common Multiple of 498 and 507