What is the Greatest Common Factor of 23584 and 23600?

Greatest common factor (GCF) of 23584 and 23600 is 16.

GCF(23584,23600) = 16

We will now calculate the prime factors of 23584 and 23600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23584 and 23600.

How to find the GCF of 23584 and 23600?

We will first find the prime factorization of 23584 and 23600. After we will calculate the factors of 23584 and 23600 and find the biggest common factor number .

Step-1: Prime Factorization of 23584

Prime factors of 23584 are 2, 11, 67. Prime factorization of 23584 in exponential form is:

23584 = 2⁵ × 11¹ × 67¹

Step-2: Prime Factorization of 23600

Prime factors of 23600 are 2, 5, 59. Prime factorization of 23600 in exponential form is:

23600 = 2⁴ × 5² × 59¹

Step-3: Factors of 23584

List of positive integer factors of 23584 that divides 23584 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 67, 88, 134, 176, 268, 352, 536, 737, 1072, 1474, 2144, 2948, 5896, 11792

Step-4: Factors of 23600

List of positive integer factors of 23600 that divides 23584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 59, 80, 100, 118, 200, 236, 295, 400, 472, 590, 944, 1180, 1475, 2360, 2950, 4720, 5900, 11800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23584 and 23600. The biggest common factor number is the GCF number.
So the greatest common factor 23584 and 23600 is 16.

Also check out the Least Common Multiple of 23584 and 23600