What is the Greatest Common Factor of 11991 and 12000?

Greatest common factor (GCF) of 11991 and 12000 is 3.

GCF(11991,12000) = 3

We will now calculate the prime factors of 11991 and 12000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11991 and 12000.

How to find the GCF of 11991 and 12000?

We will first find the prime factorization of 11991 and 12000. After we will calculate the factors of 11991 and 12000 and find the biggest common factor number .

Step-1: Prime Factorization of 11991

Prime factors of 11991 are 3, 7, 571. Prime factorization of 11991 in exponential form is:

11991 = 3¹ × 7¹ × 571¹

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 11991

List of positive integer factors of 11991 that divides 11991 without a remainder.

1, 3, 7, 21, 571, 1713, 3997

Step-4: Factors of 12000

List of positive integer factors of 12000 that divides 11991 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 11991 and 12000. The biggest common factor number is the GCF number.
So the greatest common factor 11991 and 12000 is 3.

Also check out the Least Common Multiple of 11991 and 12000