What is the Greatest Common Factor of 12000 and 12014?

Greatest common factor (GCF) of 12000 and 12014 is 2.

GCF(12000,12014) = 2

We will now calculate the prime factors of 12000 and 12014, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12000 and 12014.

How to find the GCF of 12000 and 12014?

We will first find the prime factorization of 12000 and 12014. After we will calculate the factors of 12000 and 12014 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 12014

Prime factors of 12014 are 2, 6007. Prime factorization of 12014 in exponential form is:

12014 = 2¹ × 6007¹

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 12014

List of positive integer factors of 12014 that divides 12000 without a remainder.

1, 2, 6007

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12000 and 12014. The biggest common factor number is the GCF number.
So the greatest common factor 12000 and 12014 is 2.

Also check out the Least Common Multiple of 12000 and 12014