What is the Greatest Common Factor of 12000 and 12008?

Greatest common factor (GCF) of 12000 and 12008 is 8.

GCF(12000,12008) = 8

We will now calculate the prime factors of 12000 and 12008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12000 and 12008.

How to find the GCF of 12000 and 12008?

We will first find the prime factorization of 12000 and 12008. After we will calculate the factors of 12000 and 12008 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 12008

Prime factors of 12008 are 2, 19, 79. Prime factorization of 12008 in exponential form is:

12008 = 2³ × 19¹ × 79¹

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 12008

List of positive integer factors of 12008 that divides 12000 without a remainder.

1, 2, 4, 8, 19, 38, 76, 79, 152, 158, 316, 632, 1501, 3002, 6004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12000 and 12008. The biggest common factor number is the GCF number.
So the greatest common factor 12000 and 12008 is 8.

Also check out the Least Common Multiple of 12000 and 12008