What is the Greatest Common Factor of 12000 and 12004?

Greatest common factor (GCF) of 12000 and 12004 is 4.

GCF(12000,12004) = 4

We will now calculate the prime factors of 12000 and 12004, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12000 and 12004.

How to find the GCF of 12000 and 12004?

We will first find the prime factorization of 12000 and 12004. After we will calculate the factors of 12000 and 12004 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 12004

Prime factors of 12004 are 2, 3001. Prime factorization of 12004 in exponential form is:

12004 = 2² × 3001¹

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 12004

List of positive integer factors of 12004 that divides 12000 without a remainder.

1, 2, 4, 3001, 6002

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12000 and 12004. The biggest common factor number is the GCF number.
So the greatest common factor 12000 and 12004 is 4.

Also check out the Least Common Multiple of 12000 and 12004