What is the Greatest Common Factor of 28782 and 28800?

Greatest common factor (GCF) of 28782 and 28800 is 18.

GCF(28782,28800) = 18

We will now calculate the prime factors of 28782 and 28800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28782 and 28800.

How to find the GCF of 28782 and 28800?

We will first find the prime factorization of 28782 and 28800. After we will calculate the factors of 28782 and 28800 and find the biggest common factor number .

Step-1: Prime Factorization of 28782

Prime factors of 28782 are 2, 3, 13, 41. Prime factorization of 28782 in exponential form is:

28782 = 2¹ × 3³ × 13¹ × 41¹

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 28782

List of positive integer factors of 28782 that divides 28782 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 41, 54, 78, 82, 117, 123, 234, 246, 351, 369, 533, 702, 738, 1066, 1107, 1599, 2214, 3198, 4797, 9594, 14391

Step-4: Factors of 28800

List of positive integer factors of 28800 that divides 28782 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 28782 and 28800. The biggest common factor number is the GCF number.
So the greatest common factor 28782 and 28800 is 18.

Also check out the Least Common Multiple of 28782 and 28800