What is the Greatest Common Factor of 6000 and 6012?

Greatest common factor (GCF) of 6000 and 6012 is 12.

GCF(6000,6012) = 12

We will now calculate the prime factors of 6000 and 6012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6000 and 6012.

How to find the GCF of 6000 and 6012?

We will first find the prime factorization of 6000 and 6012. After we will calculate the factors of 6000 and 6012 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 6012

Prime factors of 6012 are 2, 3, 167. Prime factorization of 6012 in exponential form is:

6012 = 2² × 3² × 167¹

Step-3: Factors of 6000

List of positive integer factors of 6000 that divides 6000 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

Step-4: Factors of 6012

List of positive integer factors of 6012 that divides 6000 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 167, 334, 501, 668, 1002, 1503, 2004, 3006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6000 and 6012. The biggest common factor number is the GCF number.
So the greatest common factor 6000 and 6012 is 12.

Also check out the Least Common Multiple of 6000 and 6012