What is the Greatest Common Factor of 12338 and 12342?

Greatest common factor (GCF) of 12338 and 12342 is 2.

GCF(12338,12342) = 2

We will now calculate the prime factors of 12338 and 12342, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12338 and 12342.

How to find the GCF of 12338 and 12342?

We will first find the prime factorization of 12338 and 12342. After we will calculate the factors of 12338 and 12342 and find the biggest common factor number .

Step-1: Prime Factorization of 12338

Prime factors of 12338 are 2, 31, 199. Prime factorization of 12338 in exponential form is:

12338 = 2¹ × 31¹ × 199¹

Step-2: Prime Factorization of 12342

Prime factors of 12342 are 2, 3, 11, 17. Prime factorization of 12342 in exponential form is:

12342 = 2¹ × 3¹ × 11² × 17¹

Step-3: Factors of 12338

List of positive integer factors of 12338 that divides 12338 without a remainder.

1, 2, 31, 62, 199, 398, 6169

Step-4: Factors of 12342

List of positive integer factors of 12342 that divides 12338 without a remainder.

1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 121, 187, 242, 363, 374, 561, 726, 1122, 2057, 4114, 6171

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12338 and 12342. The biggest common factor number is the GCF number.
So the greatest common factor 12338 and 12342 is 2.

Also check out the Least Common Multiple of 12338 and 12342