What is the Greatest Common Factor of 24000 and 24012?

Greatest common factor (GCF) of 24000 and 24012 is 12.

GCF(24000,24012) = 12

We will now calculate the prime factors of 24000 and 24012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24000 and 24012.

How to find the GCF of 24000 and 24012?

We will first find the prime factorization of 24000 and 24012. After we will calculate the factors of 24000 and 24012 and find the biggest common factor number .

Step-1: Prime Factorization of 24000

Prime factors of 24000 are 2, 3, 5. Prime factorization of 24000 in exponential form is:

24000 = 2⁶ × 3¹ × 5³

Step-2: Prime Factorization of 24012

Prime factors of 24012 are 2, 3, 23, 29. Prime factorization of 24012 in exponential form is:

24012 = 2² × 3² × 23¹ × 29¹

Step-3: Factors of 24000

List of positive integer factors of 24000 that divides 24000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 125, 150, 160, 192, 200, 240, 250, 300, 320, 375, 400, 480, 500, 600, 750, 800, 960, 1000, 1200, 1500, 1600, 2000, 2400, 3000, 4000, 4800, 6000, 8000, 12000

Step-4: Factors of 24012

List of positive integer factors of 24012 that divides 24000 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 23, 29, 36, 46, 58, 69, 87, 92, 116, 138, 174, 207, 261, 276, 348, 414, 522, 667, 828, 1044, 1334, 2001, 2668, 4002, 6003, 8004, 12006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24000 and 24012. The biggest common factor number is the GCF number.
So the greatest common factor 24000 and 24012 is 12.

Also check out the Least Common Multiple of 24000 and 24012