What is the Greatest Common Factor of 38209 and 38214?

Greatest common factor (GCF) of 38209 and 38214 is 1.

GCF(38209,38214) = 1

We will now calculate the prime factors of 38209 and 38214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38209 and 38214.

How to find the GCF of 38209 and 38214?

We will first find the prime factorization of 38209 and 38214. After we will calculate the factors of 38209 and 38214 and find the biggest common factor number .

Step-1: Prime Factorization of 38209

Prime factors of 38209 are 19, 2011. Prime factorization of 38209 in exponential form is:

38209 = 19¹ × 2011¹

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 38209

List of positive integer factors of 38209 that divides 38209 without a remainder.

1, 19, 2011

Step-4: Factors of 38214

List of positive integer factors of 38214 that divides 38209 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 38209 and 38214. The biggest common factor number is the GCF number.
So the greatest common factor 38209 and 38214 is 1.

Also check out the Least Common Multiple of 38209 and 38214