What is the Greatest Common Factor of 589 and 600?

Greatest common factor (GCF) of 589 and 600 is 1.

GCF(589,600) = 1

We will now calculate the prime factors of 589 and 600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 589 and 600.

How to find the GCF of 589 and 600?

We will first find the prime factorization of 589 and 600. After we will calculate the factors of 589 and 600 and find the biggest common factor number .

Step-1: Prime Factorization of 589

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

589 = 19¹ × 31¹

Step-2: Prime Factorization of 600

Prime factors of 600 are 2, 3, 5. Prime factorization of 600 in exponential form is:

600 = 2³ × 3¹ × 5²

Step-3: Factors of 589

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

1, 19, 31

Step-4: Factors of 600

List of positive integer factors of 600 that divides 589 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 589 and 600. The biggest common factor number is the GCF number.
So the greatest common factor 589 and 600 is 1.

Also check out the Least Common Multiple of 589 and 600