What is the Greatest Common Factor of 23200 and 23210?

Greatest common factor (GCF) of 23200 and 23210 is 10.

GCF(23200,23210) = 10

We will now calculate the prime factors of 23200 and 23210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23200 and 23210.

How to find the GCF of 23200 and 23210?

We will first find the prime factorization of 23200 and 23210. After we will calculate the factors of 23200 and 23210 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 23210

Prime factors of 23210 are 2, 5, 11, 211. Prime factorization of 23210 in exponential form is:

23210 = 2¹ × 5¹ × 11¹ × 211¹

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 23210

List of positive integer factors of 23210 that divides 23200 without a remainder.

1, 2, 5, 10, 11, 22, 55, 110, 211, 422, 1055, 2110, 2321, 4642, 11605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23200 and 23210. The biggest common factor number is the GCF number.
So the greatest common factor 23200 and 23210 is 10.

Also check out the Least Common Multiple of 23200 and 23210