What is the Greatest Common Factor of 38204 and 38214?

Greatest common factor (GCF) of 38204 and 38214 is 2.

GCF(38204,38214) = 2

We will now calculate the prime factors of 38204 and 38214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38204 and 38214.

How to find the GCF of 38204 and 38214?

We will first find the prime factorization of 38204 and 38214. After we will calculate the factors of 38204 and 38214 and find the biggest common factor number .

Step-1: Prime Factorization of 38204

Prime factors of 38204 are 2, 9551. Prime factorization of 38204 in exponential form is:

38204 = 2² × 9551¹

Step-2: Prime Factorization of 38214

Prime factors of 38214 are 2, 3, 11, 193. Prime factorization of 38214 in exponential form is:

38214 = 2¹ × 3² × 11¹ × 193¹

Step-3: Factors of 38204

List of positive integer factors of 38204 that divides 38204 without a remainder.

1, 2, 4, 9551, 19102

Step-4: Factors of 38214

List of positive integer factors of 38214 that divides 38204 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 193, 198, 386, 579, 1158, 1737, 2123, 3474, 4246, 6369, 12738, 19107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38204 and 38214. The biggest common factor number is the GCF number.
So the greatest common factor 38204 and 38214 is 2.

Also check out the Least Common Multiple of 38204 and 38214