What is the Greatest Common Factor of 338 and 356?

Greatest common factor (GCF) of 338 and 356 is 2.

GCF(338,356) = 2

We will now calculate the prime factors of 338 and 356, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 338 and 356.

How to find the GCF of 338 and 356?

We will first find the prime factorization of 338 and 356. After we will calculate the factors of 338 and 356 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 356

Prime factors of 356 are 2, 89. Prime factorization of 356 in exponential form is:

356 = 2² × 89¹

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 356

List of positive integer factors of 356 that divides 338 without a remainder.

1, 2, 4, 89, 178

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 338 and 356. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 356 is 2.

Also check out the Least Common Multiple of 338 and 356