What is the Greatest Common Factor of 589 and 608?

Greatest common factor (GCF) of 589 and 608 is 19.

GCF(589,608) = 19

We will now calculate the prime factors of 589 and 608, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 589 and 608.

How to find the GCF of 589 and 608?

We will first find the prime factorization of 589 and 608. After we will calculate the factors of 589 and 608 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 608

Prime factors of 608 are 2, 19. Prime factorization of 608 in exponential form is:

608 = 2⁵ × 19¹

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 608

List of positive integer factors of 608 that divides 589 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 589 and 608. The biggest common factor number is the GCF number.
So the greatest common factor 589 and 608 is 19.

Also check out the Least Common Multiple of 589 and 608