What is the Greatest Common Factor of 498 and 504?

Greatest common factor (GCF) of 498 and 504 is 6.

GCF(498,504) = 6

We will now calculate the prime factors of 498 and 504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 498 and 504.

How to find the GCF of 498 and 504?

We will first find the prime factorization of 498 and 504. After we will calculate the factors of 498 and 504 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 504

Prime factors of 504 are 2, 3, 7. Prime factorization of 504 in exponential form is:

504 = 2³ × 3² × 7¹

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 504

List of positive integer factors of 504 that divides 498 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 498 and 504. The biggest common factor number is the GCF number.
So the greatest common factor 498 and 504 is 6.

Also check out the Least Common Multiple of 498 and 504