What is the Greatest Common Factor of 338 and 352?

Greatest common factor (GCF) of 338 and 352 is 2.

GCF(338,352) = 2

We will now calculate the prime factors of 338 and 352, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 338 and 352.

How to find the GCF of 338 and 352?

We will first find the prime factorization of 338 and 352. After we will calculate the factors of 338 and 352 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 352

Prime factors of 352 are 2, 11. Prime factorization of 352 in exponential form is:

352 = 2⁵ × 11¹

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 352

List of positive integer factors of 352 that divides 338 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 338 and 352. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 352 is 2.

Also check out the Least Common Multiple of 338 and 352