What is the Greatest Common Factor of 23982 and 24000?

Greatest common factor (GCF) of 23982 and 24000 is 6.

GCF(23982,24000) = 6

We will now calculate the prime factors of 23982 and 24000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23982 and 24000.

How to find the GCF of 23982 and 24000?

We will first find the prime factorization of 23982 and 24000. After we will calculate the factors of 23982 and 24000 and find the biggest common factor number .

Step-1: Prime Factorization of 23982

Prime factors of 23982 are 2, 3, 7, 571. Prime factorization of 23982 in exponential form is:

23982 = 2¹ × 3¹ × 7¹ × 571¹

Step-2: 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-3: Factors of 23982

List of positive integer factors of 23982 that divides 23982 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 571, 1142, 1713, 3426, 3997, 7994, 11991

Step-4: Factors of 24000

List of positive integer factors of 24000 that divides 23982 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23982 and 24000. The biggest common factor number is the GCF number.
So the greatest common factor 23982 and 24000 is 6.

Also check out the Least Common Multiple of 23982 and 24000