What is the Greatest Common Factor of 48000 and 48009?

Greatest common factor (GCF) of 48000 and 48009 is 3.

GCF(48000,48009) = 3

We will now calculate the prime factors of 48000 and 48009, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48000 and 48009.

How to find the GCF of 48000 and 48009?

We will first find the prime factorization of 48000 and 48009. After we will calculate the factors of 48000 and 48009 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 48009

Prime factors of 48009 are 3, 13, 1231. Prime factorization of 48009 in exponential form is:

48009 = 3¹ × 13¹ × 1231¹

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 48009

List of positive integer factors of 48009 that divides 48000 without a remainder.

1, 3, 13, 39, 1231, 3693, 16003

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48000 and 48009. The biggest common factor number is the GCF number.
So the greatest common factor 48000 and 48009 is 3.

Also check out the Least Common Multiple of 48000 and 48009