What is the Greatest Common Factor of 338 and 342?

Greatest common factor (GCF) of 338 and 342 is 2.

GCF(338,342) = 2

We will now calculate the prime factors of 338 and 342, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 338 and 342.

How to find the GCF of 338 and 342?

We will first find the prime factorization of 338 and 342. After we will calculate the factors of 338 and 342 and find the biggest common factor number .

Step-1: Prime Factorization of 338

Prime factors of 338 are 2, 13. Prime factorization of 338 in exponential form is:

338 = 2¹ × 13²

Step-2: Prime Factorization of 342

Prime factors of 342 are 2, 3, 19. Prime factorization of 342 in exponential form is:

342 = 2¹ × 3² × 19¹

Step-3: Factors of 338

List of positive integer factors of 338 that divides 338 without a remainder.

1, 2, 13, 26, 169

Step-4: Factors of 342

List of positive integer factors of 342 that divides 338 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 338 and 342. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 342 is 2.

Also check out the Least Common Multiple of 338 and 342