What is the Greatest Common Factor of 12000 and 12012?

Greatest common factor (GCF) of 12000 and 12012 is 12.

GCF(12000,12012) = 12

We will now calculate the prime factors of 12000 and 12012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12000 and 12012.

How to find the GCF of 12000 and 12012?

We will first find the prime factorization of 12000 and 12012. After we will calculate the factors of 12000 and 12012 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 12012

Prime factors of 12012 are 2, 3, 7, 11, 13. Prime factorization of 12012 in exponential form is:

12012 = 2² × 3¹ × 7¹ × 11¹ × 13¹

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 12012

List of positive integer factors of 12012 that divides 12000 without a remainder.

1, 2, 3, 4, 6, 7, 11, 12, 13, 14, 21, 22, 26, 28, 33, 39, 42, 44, 52, 66, 77, 78, 84, 91, 132, 143, 154, 156, 182, 231, 273, 286, 308, 364, 429, 462, 546, 572, 858, 924, 1001, 1092, 1716, 2002, 3003, 4004, 6006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12000 and 12012. The biggest common factor number is the GCF number.
So the greatest common factor 12000 and 12012 is 12.

Also check out the Least Common Multiple of 12000 and 12012