What is the Greatest Common Factor of 47994 and 48000?

Greatest common factor (GCF) of 47994 and 48000 is 6.

GCF(47994,48000) = 6

We will now calculate the prime factors of 47994 and 48000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47994 and 48000.

How to find the GCF of 47994 and 48000?

We will first find the prime factorization of 47994 and 48000. After we will calculate the factors of 47994 and 48000 and find the biggest common factor number .

Step-1: Prime Factorization of 47994

Prime factors of 47994 are 2, 3, 19, 421. Prime factorization of 47994 in exponential form is:

47994 = 2¹ × 3¹ × 19¹ × 421¹

Step-2: Prime Factorization of 48000

Prime factors of 48000 are 2, 3, 5. Prime factorization of 48000 in exponential form is:

48000 = 2⁷ × 3¹ × 5³

Step-3: Factors of 47994

List of positive integer factors of 47994 that divides 47994 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 421, 842, 1263, 2526, 7999, 15998, 23997

Step-4: Factors of 48000

List of positive integer factors of 48000 that divides 47994 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, 128, 150, 160, 192, 200, 240, 250, 300, 320, 375, 384, 400, 480, 500, 600, 640, 750, 800, 960, 1000, 1200, 1500, 1600, 1920, 2000, 2400, 3000, 3200, 4000, 4800, 6000, 8000, 9600, 12000, 16000, 24000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47994 and 48000. The biggest common factor number is the GCF number.
So the greatest common factor 47994 and 48000 is 6.

Also check out the Least Common Multiple of 47994 and 48000