What is the Greatest Common Factor of 334 and 343?

Greatest common factor (GCF) of 334 and 343 is 1.

GCF(334,343) = 1

We will now calculate the prime factors of 334 and 343, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 334 and 343.

How to find the GCF of 334 and 343?

We will first find the prime factorization of 334 and 343. After we will calculate the factors of 334 and 343 and find the biggest common factor number .

Step-1: Prime Factorization of 334

Prime factors of 334 are 2, 167. Prime factorization of 334 in exponential form is:

334 = 2¹ × 167¹

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 334

List of positive integer factors of 334 that divides 334 without a remainder.

1, 2, 167

Step-4: Factors of 343

List of positive integer factors of 343 that divides 334 without a remainder.

1, 7, 49

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 334 and 343. The biggest common factor number is the GCF number.
So the greatest common factor 334 and 343 is 1.

Also check out the Least Common Multiple of 334 and 343