What is the Greatest Common Factor of 23200 and 23214?

Greatest common factor (GCF) of 23200 and 23214 is 2.

GCF(23200,23214) = 2

We will now calculate the prime factors of 23200 and 23214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23200 and 23214.

How to find the GCF of 23200 and 23214?

We will first find the prime factorization of 23200 and 23214. After we will calculate the factors of 23200 and 23214 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 23214

Prime factors of 23214 are 2, 3, 53, 73. Prime factorization of 23214 in exponential form is:

23214 = 2¹ × 3¹ × 53¹ × 73¹

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 23214

List of positive integer factors of 23214 that divides 23200 without a remainder.

1, 2, 3, 6, 53, 73, 106, 146, 159, 219, 318, 438, 3869, 7738, 11607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23200 and 23214. The biggest common factor number is the GCF number.
So the greatest common factor 23200 and 23214 is 2.

Also check out the Least Common Multiple of 23200 and 23214