What is the Greatest Common Factor of 28780 and 28800?

Greatest common factor (GCF) of 28780 and 28800 is 20.

GCF(28780,28800) = 20

We will now calculate the prime factors of 28780 and 28800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28780 and 28800.

How to find the GCF of 28780 and 28800?

We will first find the prime factorization of 28780 and 28800. After we will calculate the factors of 28780 and 28800 and find the biggest common factor number .

Step-1: Prime Factorization of 28780

Prime factors of 28780 are 2, 5, 1439. Prime factorization of 28780 in exponential form is:

28780 = 2² × 5¹ × 1439¹

Step-2: 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-3: Factors of 28780

List of positive integer factors of 28780 that divides 28780 without a remainder.

1, 2, 4, 5, 10, 20, 1439, 2878, 5756, 7195, 14390

Step-4: Factors of 28800

List of positive integer factors of 28800 that divides 28780 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28780 and 28800. The biggest common factor number is the GCF number.
So the greatest common factor 28780 and 28800 is 20.

Also check out the Least Common Multiple of 28780 and 28800