What is the Greatest Common Factor of 23200 and 23205?

Greatest common factor (GCF) of 23200 and 23205 is 5.

GCF(23200,23205) = 5

We will now calculate the prime factors of 23200 and 23205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23200 and 23205.

How to find the GCF of 23200 and 23205?

We will first find the prime factorization of 23200 and 23205. After we will calculate the factors of 23200 and 23205 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 23205

Prime factors of 23205 are 3, 5, 7, 13, 17. Prime factorization of 23205 in exponential form is:

23205 = 3¹ × 5¹ × 7¹ × 13¹ × 17¹

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 23205

List of positive integer factors of 23205 that divides 23200 without a remainder.

1, 3, 5, 7, 13, 15, 17, 21, 35, 39, 51, 65, 85, 91, 105, 119, 195, 221, 255, 273, 357, 455, 595, 663, 1105, 1365, 1547, 1785, 3315, 4641, 7735

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23200 and 23205. The biggest common factor number is the GCF number.
So the greatest common factor 23200 and 23205 is 5.

Also check out the Least Common Multiple of 23200 and 23205