What is the Greatest Common Factor of 11385 and 11400?

Greatest common factor (GCF) of 11385 and 11400 is 15.

GCF(11385,11400) = 15

We will now calculate the prime factors of 11385 and 11400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11385 and 11400.

How to find the GCF of 11385 and 11400?

We will first find the prime factorization of 11385 and 11400. After we will calculate the factors of 11385 and 11400 and find the biggest common factor number .

Step-1: Prime Factorization of 11385

Prime factors of 11385 are 3, 5, 11, 23. Prime factorization of 11385 in exponential form is:

11385 = 3² × 5¹ × 11¹ × 23¹

Step-2: Prime Factorization of 11400

Prime factors of 11400 are 2, 3, 5, 19. Prime factorization of 11400 in exponential form is:

11400 = 2³ × 3¹ × 5² × 19¹

Step-3: Factors of 11385

List of positive integer factors of 11385 that divides 11385 without a remainder.

1, 3, 5, 9, 11, 15, 23, 33, 45, 55, 69, 99, 115, 165, 207, 253, 345, 495, 759, 1035, 1265, 2277, 3795

Step-4: Factors of 11400

List of positive integer factors of 11400 that divides 11385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 25, 30, 38, 40, 50, 57, 60, 75, 76, 95, 100, 114, 120, 150, 152, 190, 200, 228, 285, 300, 380, 456, 475, 570, 600, 760, 950, 1140, 1425, 1900, 2280, 2850, 3800, 5700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11385 and 11400. The biggest common factor number is the GCF number.
So the greatest common factor 11385 and 11400 is 15.

Also check out the Least Common Multiple of 11385 and 11400