What is the Greatest Common Factor of 585 and 600?

Greatest common factor (GCF) of 585 and 600 is 15.

GCF(585,600) = 15

We will now calculate the prime factors of 585 and 600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 585 and 600.

How to find the GCF of 585 and 600?

We will first find the prime factorization of 585 and 600. After we will calculate the factors of 585 and 600 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 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 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 600

List of positive integer factors of 600 that divides 585 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 585 and 600. The biggest common factor number is the GCF number.
So the greatest common factor 585 and 600 is 15.

Also check out the Least Common Multiple of 585 and 600