What is the Greatest Common Factor of 11584 and 11600?

Greatest common factor (GCF) of 11584 and 11600 is 16.

GCF(11584,11600) = 16

We will now calculate the prime factors of 11584 and 11600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11584 and 11600.

How to find the GCF of 11584 and 11600?

We will first find the prime factorization of 11584 and 11600. After we will calculate the factors of 11584 and 11600 and find the biggest common factor number .

Step-1: Prime Factorization of 11584

Prime factors of 11584 are 2, 181. Prime factorization of 11584 in exponential form is:

11584 = 2⁶ × 181¹

Step-2: Prime Factorization of 11600

Prime factors of 11600 are 2, 5, 29. Prime factorization of 11600 in exponential form is:

11600 = 2⁴ × 5² × 29¹

Step-3: Factors of 11584

List of positive integer factors of 11584 that divides 11584 without a remainder.

1, 2, 4, 8, 16, 32, 64, 181, 362, 724, 1448, 2896, 5792

Step-4: Factors of 11600

List of positive integer factors of 11600 that divides 11584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 40, 50, 58, 80, 100, 116, 145, 200, 232, 290, 400, 464, 580, 725, 1160, 1450, 2320, 2900, 5800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11584 and 11600. The biggest common factor number is the GCF number.
So the greatest common factor 11584 and 11600 is 16.

Also check out the Least Common Multiple of 11584 and 11600