What is the Greatest Common Factor of 497 and 504?

Greatest common factor (GCF) of 497 and 504 is 7.

GCF(497,504) = 7

We will now calculate the prime factors of 497 and 504, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 497 and 504.

How to find the GCF of 497 and 504?

We will first find the prime factorization of 497 and 504. After we will calculate the factors of 497 and 504 and find the biggest common factor number .

Step-1: Prime Factorization of 497

Prime factors of 497 are 7, 71. Prime factorization of 497 in exponential form is:

497 = 7¹ × 71¹

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 497

List of positive integer factors of 497 that divides 497 without a remainder.

1, 7, 71

Step-4: Factors of 504

List of positive integer factors of 504 that divides 497 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 497 and 504. The biggest common factor number is the GCF number.
So the greatest common factor 497 and 504 is 7.

Also check out the Least Common Multiple of 497 and 504