What is the Greatest Common Factor of 585 and 596?

Greatest common factor (GCF) of 585 and 596 is 1.

GCF(585,596) = 1

We will now calculate the prime factors of 585 and 596, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 585 and 596.

How to find the GCF of 585 and 596?

We will first find the prime factorization of 585 and 596. After we will calculate the factors of 585 and 596 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 596

Prime factors of 596 are 2, 149. Prime factorization of 596 in exponential form is:

596 = 2² × 149¹

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 596

List of positive integer factors of 596 that divides 585 without a remainder.

1, 2, 4, 149, 298

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 585 and 596. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 596 is 1.

Also check out the Least Common Multiple of 585 and 596