What is the Greatest Common Factor of 12000 and 12006?

Greatest common factor (GCF) of 12000 and 12006 is 6.

GCF(12000,12006) = 6

We will now calculate the prime factors of 12000 and 12006, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12000 and 12006.

How to find the GCF of 12000 and 12006?

We will first find the prime factorization of 12000 and 12006. After we will calculate the factors of 12000 and 12006 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12006

Prime factors of 12006 are 2, 3, 23, 29. Prime factorization of 12006 in exponential form is:

12006 = 2¹ × 3² × 23¹ × 29¹

Step-3: Factors of 12000

List of positive integer factors of 12000 that divides 12000 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

Step-4: Factors of 12006

List of positive integer factors of 12006 that divides 12000 without a remainder.

1, 2, 3, 6, 9, 18, 23, 29, 46, 58, 69, 87, 138, 174, 207, 261, 414, 522, 667, 1334, 2001, 4002, 6003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12000 and 12006. The biggest common factor number is the GCF number.
So the greatest common factor 12000 and 12006 is 6.

Also check out the Least Common Multiple of 12000 and 12006