What is the Greatest Common Factor of 48000 and 48020?

Greatest common factor (GCF) of 48000 and 48020 is 20.

GCF(48000,48020) = 20

We will now calculate the prime factors of 48000 and 48020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48000 and 48020.

How to find the GCF of 48000 and 48020?

We will first find the prime factorization of 48000 and 48020. After we will calculate the factors of 48000 and 48020 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 48020

Prime factors of 48020 are 2, 5, 7. Prime factorization of 48020 in exponential form is:

48020 = 2² × 5¹ × 7⁴

Step-3: Factors of 48000

List of positive integer factors of 48000 that divides 48000 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

Step-4: Factors of 48020

List of positive integer factors of 48020 that divides 48000 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 343, 490, 686, 980, 1372, 1715, 2401, 3430, 4802, 6860, 9604, 12005, 24010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48000 and 48020. The biggest common factor number is the GCF number.
So the greatest common factor 48000 and 48020 is 20.

Also check out the Least Common Multiple of 48000 and 48020