What is the Greatest Common Factor of 28800 and 28814?

Greatest common factor (GCF) of 28800 and 28814 is 2.

GCF(28800,28814) = 2

We will now calculate the prime factors of 28800 and 28814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28800 and 28814.

How to find the GCF of 28800 and 28814?

We will first find the prime factorization of 28800 and 28814. After we will calculate the factors of 28800 and 28814 and find the biggest common factor number .

Step-1: Prime Factorization of 28800

Prime factors of 28800 are 2, 3, 5. Prime factorization of 28800 in exponential form is:

28800 = 2⁷ × 3² × 5²

Step-2: Prime Factorization of 28814

Prime factors of 28814 are 2, 14407. Prime factorization of 28814 in exponential form is:

28814 = 2¹ × 14407¹

Step-3: Factors of 28800

List of positive integer factors of 28800 that divides 28800 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900, 960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800, 5760, 7200, 9600, 14400

Step-4: Factors of 28814

List of positive integer factors of 28814 that divides 28800 without a remainder.

1, 2, 14407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28800 and 28814. The biggest common factor number is the GCF number.
So the greatest common factor 28800 and 28814 is 2.

Also check out the Least Common Multiple of 28800 and 28814