What is the Greatest Common Factor of 47984 and 48000?

Greatest common factor (GCF) of 47984 and 48000 is 16.

GCF(47984,48000) = 16

We will now calculate the prime factors of 47984 and 48000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47984 and 48000.

How to find the GCF of 47984 and 48000?

We will first find the prime factorization of 47984 and 48000. After we will calculate the factors of 47984 and 48000 and find the biggest common factor number .

Step-1: Prime Factorization of 47984

Prime factors of 47984 are 2, 2999. Prime factorization of 47984 in exponential form is:

47984 = 2⁴ × 2999¹

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 47984

List of positive integer factors of 47984 that divides 47984 without a remainder.

1, 2, 4, 8, 16, 2999, 5998, 11996, 23992

Step-4: Factors of 48000

List of positive integer factors of 48000 that divides 47984 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 47984 and 48000. The biggest common factor number is the GCF number.
So the greatest common factor 47984 and 48000 is 16.

Also check out the Least Common Multiple of 47984 and 48000