What is the Greatest Common Factor of 11985 and 12000?

Greatest common factor (GCF) of 11985 and 12000 is 15.

GCF(11985,12000) = 15

We will now calculate the prime factors of 11985 and 12000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11985 and 12000.

How to find the GCF of 11985 and 12000?

We will first find the prime factorization of 11985 and 12000. After we will calculate the factors of 11985 and 12000 and find the biggest common factor number .

Step-1: Prime Factorization of 11985

Prime factors of 11985 are 3, 5, 17, 47. Prime factorization of 11985 in exponential form is:

11985 = 3¹ × 5¹ × 17¹ × 47¹

Step-2: Prime Factorization of 12000

Prime factors of 12000 are 2, 3, 5. Prime factorization of 12000 in exponential form is:

12000 = 2⁵ × 3¹ × 5³

Step-3: Factors of 11985

List of positive integer factors of 11985 that divides 11985 without a remainder.

1, 3, 5, 15, 17, 47, 51, 85, 141, 235, 255, 705, 799, 2397, 3995

Step-4: Factors of 12000

List of positive integer factors of 12000 that divides 11985 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 125, 150, 160, 200, 240, 250, 300, 375, 400, 480, 500, 600, 750, 800, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11985 and 12000. The biggest common factor number is the GCF number.
So the greatest common factor 11985 and 12000 is 15.

Also check out the Least Common Multiple of 11985 and 12000