What is the Greatest Common Factor of 338 and 349?

Greatest common factor (GCF) of 338 and 349 is 1.

GCF(338,349) = 1

We will now calculate the prime factors of 338 and 349, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 338 and 349.

How to find the GCF of 338 and 349?

We will first find the prime factorization of 338 and 349. After we will calculate the factors of 338 and 349 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 349

Prime factors of 349 are 349. Prime factorization of 349 in exponential form is:

349 = 349¹

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 349

List of positive integer factors of 349 that divides 338 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 338 and 349. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 349 is 1.

Also check out the Least Common Multiple of 338 and 349