What is the Greatest Common Factor of 584 and 589?

Greatest common factor (GCF) of 584 and 589 is 1.

GCF(584,589) = 1

We will now calculate the prime factors of 584 and 589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 584 and 589.

How to find the GCF of 584 and 589?

We will first find the prime factorization of 584 and 589. After we will calculate the factors of 584 and 589 and find the biggest common factor number .

Step-1: Prime Factorization of 584

Prime factors of 584 are 2, 73. Prime factorization of 584 in exponential form is:

584 = 2³ × 73¹

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 584

List of positive integer factors of 584 that divides 584 without a remainder.

1, 2, 4, 8, 73, 146, 292

Step-4: Factors of 589

List of positive integer factors of 589 that divides 584 without a remainder.

1, 19, 31

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 584 and 589. The biggest common factor number is the GCF number.
So the greatest common factor 584 and 589 is 1.

Also check out the Least Common Multiple of 584 and 589