What is the Greatest Common Factor of 338 and 350?

Greatest common factor (GCF) of 338 and 350 is 2.

GCF(338,350) = 2

We will now calculate the prime factors of 338 and 350, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 338 and 350.

How to find the GCF of 338 and 350?

We will first find the prime factorization of 338 and 350. After we will calculate the factors of 338 and 350 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 350

Prime factors of 350 are 2, 5, 7. Prime factorization of 350 in exponential form is:

350 = 2¹ × 5² × 7¹

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 350

List of positive integer factors of 350 that divides 338 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 338 and 350. The biggest common factor number is the GCF number.
So the greatest common factor 338 and 350 is 2.

Also check out the Least Common Multiple of 338 and 350