What is the Greatest Common Factor of 28800 and 28815?

Greatest common factor (GCF) of 28800 and 28815 is 15.

GCF(28800,28815) = 15

We will now calculate the prime factors of 28800 and 28815, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28800 and 28815.

How to find the GCF of 28800 and 28815?

We will first find the prime factorization of 28800 and 28815. After we will calculate the factors of 28800 and 28815 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 28815

Prime factors of 28815 are 3, 5, 17, 113. Prime factorization of 28815 in exponential form is:

28815 = 3¹ × 5¹ × 17¹ × 113¹

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 28815

List of positive integer factors of 28815 that divides 28800 without a remainder.

1, 3, 5, 15, 17, 51, 85, 113, 255, 339, 565, 1695, 1921, 5763, 9605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28800 and 28815. The biggest common factor number is the GCF number.
So the greatest common factor 28800 and 28815 is 15.

Also check out the Least Common Multiple of 28800 and 28815