What is the Greatest Common Factor of 585 and 597?

Greatest common factor (GCF) of 585 and 597 is 3.

GCF(585,597) = 3

We will now calculate the prime factors of 585 and 597, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 585 and 597.

How to find the GCF of 585 and 597?

We will first find the prime factorization of 585 and 597. After we will calculate the factors of 585 and 597 and find the biggest common factor number .

Step-1: Prime Factorization of 585

Prime factors of 585 are 3, 5, 13. Prime factorization of 585 in exponential form is:

585 = 3² × 5¹ × 13¹

Step-2: Prime Factorization of 597

Prime factors of 597 are 3, 199. Prime factorization of 597 in exponential form is:

597 = 3¹ × 199¹

Step-3: Factors of 585

List of positive integer factors of 585 that divides 585 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195

Step-4: Factors of 597

List of positive integer factors of 597 that divides 585 without a remainder.

1, 3, 199

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 585 and 597. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 597 is 3.

Also check out the Least Common Multiple of 585 and 597