What is the Greatest Common Factor of 23200 and 23209?

Greatest common factor (GCF) of 23200 and 23209 is 1.

GCF(23200,23209) = 1

We will now calculate the prime factors of 23200 and 23209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23200 and 23209.

How to find the GCF of 23200 and 23209?

We will first find the prime factorization of 23200 and 23209. After we will calculate the factors of 23200 and 23209 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 23209

Prime factors of 23209 are 23209. Prime factorization of 23209 in exponential form is:

23209 = 23209¹

Step-3: Factors of 23200

List of positive integer factors of 23200 that divides 23200 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

Step-4: Factors of 23209

List of positive integer factors of 23209 that divides 23200 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23200 and 23209. The biggest common factor number is the GCF number.
So the greatest common factor 23200 and 23209 is 1.

Also check out the Least Common Multiple of 23200 and 23209