What is the Greatest Common Factor of 34304 and 34322?

Greatest common factor (GCF) of 34304 and 34322 is 2.

GCF(34304,34322) = 2

We will now calculate the prime factors of 34304 and 34322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34304 and 34322.

How to find the GCF of 34304 and 34322?

We will first find the prime factorization of 34304 and 34322. After we will calculate the factors of 34304 and 34322 and find the biggest common factor number .

Step-1: Prime Factorization of 34304

Prime factors of 34304 are 2, 67. Prime factorization of 34304 in exponential form is:

34304 = 2⁹ × 67¹

Step-2: Prime Factorization of 34322

Prime factors of 34322 are 2, 131. Prime factorization of 34322 in exponential form is:

34322 = 2¹ × 131²

Step-3: Factors of 34304

List of positive integer factors of 34304 that divides 34304 without a remainder.

1, 2, 4, 8, 16, 32, 64, 67, 128, 134, 256, 268, 512, 536, 1072, 2144, 4288, 8576, 17152

Step-4: Factors of 34322

List of positive integer factors of 34322 that divides 34304 without a remainder.

1, 2, 131, 262, 17161

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34304 and 34322. The biggest common factor number is the GCF number.
So the greatest common factor 34304 and 34322 is 2.

Also check out the Least Common Multiple of 34304 and 34322