What is the Greatest Common Factor of 23188 and 23200?

Greatest common factor (GCF) of 23188 and 23200 is 4.

GCF(23188,23200) = 4

We will now calculate the prime factors of 23188 and 23200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23188 and 23200.

How to find the GCF of 23188 and 23200?

We will first find the prime factorization of 23188 and 23200. After we will calculate the factors of 23188 and 23200 and find the biggest common factor number .

Step-1: Prime Factorization of 23188

Prime factors of 23188 are 2, 11, 17, 31. Prime factorization of 23188 in exponential form is:

23188 = 2² × 11¹ × 17¹ × 31¹

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 23188

List of positive integer factors of 23188 that divides 23188 without a remainder.

1, 2, 4, 11, 17, 22, 31, 34, 44, 62, 68, 124, 187, 341, 374, 527, 682, 748, 1054, 1364, 2108, 5797, 11594

Step-4: Factors of 23200

List of positive integer factors of 23200 that divides 23188 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 23188 and 23200. The biggest common factor number is the GCF number.
So the greatest common factor 23188 and 23200 is 4.

Also check out the Least Common Multiple of 23188 and 23200