What is the Greatest Common Factor of 319 and 338?

Greatest common factor (GCF) of 319 and 338 is 1.

GCF(319,338) = 1

We will now calculate the prime factors of 319 and 338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 319 and 338.

How to find the GCF of 319 and 338?

We will first find the prime factorization of 319 and 338. After we will calculate the factors of 319 and 338 and find the biggest common factor number .

Step-1: Prime Factorization of 319

Prime factors of 319 are 11, 29. Prime factorization of 319 in exponential form is:

319 = 11¹ × 29¹

Step-2: Prime Factorization of 338

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

338 = 2¹ × 13²

Step-3: Factors of 319

List of positive integer factors of 319 that divides 319 without a remainder.

1, 11, 29

Step-4: Factors of 338

List of positive integer factors of 338 that divides 319 without a remainder.

1, 2, 13, 26, 169

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 319 and 338. The biggest common factor number is the GCF number.
So the greatest common factor 319 and 338 is 1.

Also check out the Least Common Multiple of 319 and 338