What is the Greatest Common Factor of 12000 and 12005?

Greatest common factor (GCF) of 12000 and 12005 is 5.

GCF(12000,12005) = 5

We will now calculate the prime factors of 12000 and 12005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12000 and 12005.

How to find the GCF of 12000 and 12005?

We will first find the prime factorization of 12000 and 12005. After we will calculate the factors of 12000 and 12005 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 12005

Prime factors of 12005 are 5, 7. Prime factorization of 12005 in exponential form is:

12005 = 5¹ × 7⁴

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 12005

List of positive integer factors of 12005 that divides 12000 without a remainder.

1, 5, 7, 35, 49, 245, 343, 1715, 2401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12000 and 12005. The biggest common factor number is the GCF number.
So the greatest common factor 12000 and 12005 is 5.

Also check out the Least Common Multiple of 12000 and 12005