What is the Greatest Common Factor of 5985 and 6000?

Greatest common factor (GCF) of 5985 and 6000 is 15.

GCF(5985,6000) = 15

We will now calculate the prime factors of 5985 and 6000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5985 and 6000.

How to find the GCF of 5985 and 6000?

We will first find the prime factorization of 5985 and 6000. After we will calculate the factors of 5985 and 6000 and find the biggest common factor number .

Step-1: Prime Factorization of 5985

Prime factors of 5985 are 3, 5, 7, 19. Prime factorization of 5985 in exponential form is:

5985 = 3² × 5¹ × 7¹ × 19¹

Step-2: Prime Factorization of 6000

Prime factors of 6000 are 2, 3, 5. Prime factorization of 6000 in exponential form is:

6000 = 2⁴ × 3¹ × 5³

Step-3: Factors of 5985

List of positive integer factors of 5985 that divides 5985 without a remainder.

1, 3, 5, 7, 9, 15, 19, 21, 35, 45, 57, 63, 95, 105, 133, 171, 285, 315, 399, 665, 855, 1197, 1995

Step-4: Factors of 6000

List of positive integer factors of 6000 that divides 5985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5985 and 6000. The biggest common factor number is the GCF number.
So the greatest common factor 5985 and 6000 is 15.

Also check out the Least Common Multiple of 5985 and 6000