What is the Greatest Common Factor of 28785 and 28800?

Greatest common factor (GCF) of 28785 and 28800 is 15.

GCF(28785,28800) = 15

We will now calculate the prime factors of 28785 and 28800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28785 and 28800.

How to find the GCF of 28785 and 28800?

We will first find the prime factorization of 28785 and 28800. After we will calculate the factors of 28785 and 28800 and find the biggest common factor number .

Step-1: Prime Factorization of 28785

Prime factors of 28785 are 3, 5, 19, 101. Prime factorization of 28785 in exponential form is:

28785 = 3¹ × 5¹ × 19¹ × 101¹

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 28785

List of positive integer factors of 28785 that divides 28785 without a remainder.

1, 3, 5, 15, 19, 57, 95, 101, 285, 303, 505, 1515, 1919, 5757, 9595

Step-4: Factors of 28800

List of positive integer factors of 28800 that divides 28785 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 28785 and 28800. The biggest common factor number is the GCF number.
So the greatest common factor 28785 and 28800 is 15.

Also check out the Least Common Multiple of 28785 and 28800