What is the Greatest Common Factor of 34288 and 34304?

Greatest common factor (GCF) of 34288 and 34304 is 16.

GCF(34288,34304) = 16

We will now calculate the prime factors of 34288 and 34304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34288 and 34304.

How to find the GCF of 34288 and 34304?

We will first find the prime factorization of 34288 and 34304. After we will calculate the factors of 34288 and 34304 and find the biggest common factor number .

Step-1: Prime Factorization of 34288

Prime factors of 34288 are 2, 2143. Prime factorization of 34288 in exponential form is:

34288 = 2⁴ × 2143¹

Step-2: Prime Factorization of 34304

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

34304 = 2⁹ × 67¹

Step-3: Factors of 34288

List of positive integer factors of 34288 that divides 34288 without a remainder.

1, 2, 4, 8, 16, 2143, 4286, 8572, 17144

Step-4: Factors of 34304

List of positive integer factors of 34304 that divides 34288 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34288 and 34304. The biggest common factor number is the GCF number.
So the greatest common factor 34288 and 34304 is 16.

Also check out the Least Common Multiple of 34288 and 34304