What is the Greatest Common Factor of 23184 and 23200?

Greatest common factor (GCF) of 23184 and 23200 is 16.

GCF(23184,23200) = 16

We will now calculate the prime factors of 23184 and 23200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23184 and 23200.

How to find the GCF of 23184 and 23200?

We will first find the prime factorization of 23184 and 23200. After we will calculate the factors of 23184 and 23200 and find the biggest common factor number .

Step-1: Prime Factorization of 23184

Prime factors of 23184 are 2, 3, 7, 23. Prime factorization of 23184 in exponential form is:

23184 = 2⁴ × 3² × 7¹ × 23¹

Step-2: Prime Factorization of 23200

Prime factors of 23200 are 2, 5, 29. Prime factorization of 23200 in exponential form is:

23200 = 2⁵ × 5² × 29¹

Step-3: Factors of 23184

List of positive integer factors of 23184 that divides 23184 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 23, 24, 28, 36, 42, 46, 48, 56, 63, 69, 72, 84, 92, 112, 126, 138, 144, 161, 168, 184, 207, 252, 276, 322, 336, 368, 414, 483, 504, 552, 644, 828, 966, 1008, 1104, 1288, 1449, 1656, 1932, 2576, 2898, 3312, 3864, 5796, 7728, 11592

Step-4: Factors of 23200

List of positive integer factors of 23200 that divides 23184 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 29, 32, 40, 50, 58, 80, 100, 116, 145, 160, 200, 232, 290, 400, 464, 580, 725, 800, 928, 1160, 1450, 2320, 2900, 4640, 5800, 11600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23184 and 23200. The biggest common factor number is the GCF number.
So the greatest common factor 23184 and 23200 is 16.

Also check out the Least Common Multiple of 23184 and 23200