What is the Greatest Common Factor of 585 and 589?

Greatest common factor (GCF) of 585 and 589 is 1.

GCF(585,589) = 1

We will now calculate the prime factors of 585 and 589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 585 and 589.

How to find the GCF of 585 and 589?

We will first find the prime factorization of 585 and 589. After we will calculate the factors of 585 and 589 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 589

Prime factors of 589 are 19, 31. Prime factorization of 589 in exponential form is:

589 = 19¹ × 31¹

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 589

List of positive integer factors of 589 that divides 585 without a remainder.

1, 19, 31

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 585 and 589. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 589 is 1.

Also check out the Least Common Multiple of 585 and 589