What is the Greatest Common Factor of 330 and 338?

Greatest common factor (GCF) of 330 and 338 is 2.

GCF(330,338) = 2

We will now calculate the prime factors of 330 and 338, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 330 and 338.

How to find the GCF of 330 and 338?

We will first find the prime factorization of 330 and 338. After we will calculate the factors of 330 and 338 and find the biggest common factor number .

Step-1: Prime Factorization of 330

Prime factors of 330 are 2, 3, 5, 11. Prime factorization of 330 in exponential form is:

330 = 2¹ × 3¹ × 5¹ × 11¹

Step-2: Prime Factorization of 338

Prime factors of 338 are 2, 13. Prime factorization of 338 in exponential form is:

338 = 2¹ × 13²

Step-3: Factors of 330

List of positive integer factors of 330 that divides 330 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165

Step-4: Factors of 338

List of positive integer factors of 338 that divides 330 without a remainder.

1, 2, 13, 26, 169

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 330 and 338. The biggest common factor number is the GCF number.
So the greatest common factor 330 and 338 is 2.

Also check out the Least Common Multiple of 330 and 338