What is the Greatest Common Factor of 600 and 609?

Greatest common factor (GCF) of 600 and 609 is 3.

GCF(600,609) = 3

We will now calculate the prime factors of 600 and 609, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 600 and 609.

How to find the GCF of 600 and 609?

We will first find the prime factorization of 600 and 609. After we will calculate the factors of 600 and 609 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 609

Prime factors of 609 are 3, 7, 29. Prime factorization of 609 in exponential form is:

609 = 3¹ × 7¹ × 29¹

Step-3: Factors of 600

List of positive integer factors of 600 that divides 600 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

Step-4: Factors of 609

List of positive integer factors of 609 that divides 600 without a remainder.

1, 3, 7, 21, 29, 87, 203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 600 and 609. The biggest common factor number is the GCF number.
So the greatest common factor 600 and 609 is 3.

Also check out the Least Common Multiple of 600 and 609