What is the Greatest Common Factor of 338 and 343?

Greatest common factor (GCF) of 338 and 343 is 1.

GCF(338,343) = 1

We will now calculate the prime factors of 338 and 343, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 338 and 343.

How to find the GCF of 338 and 343?

We will first find the prime factorization of 338 and 343. After we will calculate the factors of 338 and 343 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 343

Prime factors of 343 are 7. Prime factorization of 343 in exponential form is:

343 = 7³

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 343

List of positive integer factors of 343 that divides 338 without a remainder.

1, 7, 49

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 338 and 343. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 343 is 1.

Also check out the Least Common Multiple of 338 and 343