What is the Greatest Common Factor of 34286 and 34304?

Greatest common factor (GCF) of 34286 and 34304 is 2.

GCF(34286,34304) = 2

We will now calculate the prime factors of 34286 and 34304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34286 and 34304.

How to find the GCF of 34286 and 34304?

We will first find the prime factorization of 34286 and 34304. After we will calculate the factors of 34286 and 34304 and find the biggest common factor number .

Step-1: Prime Factorization of 34286

Prime factors of 34286 are 2, 7, 31, 79. Prime factorization of 34286 in exponential form is:

34286 = 2¹ × 7¹ × 31¹ × 79¹

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 34286

List of positive integer factors of 34286 that divides 34286 without a remainder.

1, 2, 7, 14, 31, 62, 79, 158, 217, 434, 553, 1106, 2449, 4898, 17143

Step-4: Factors of 34304

List of positive integer factors of 34304 that divides 34286 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 34286 and 34304. The biggest common factor number is the GCF number.
So the greatest common factor 34286 and 34304 is 2.

Also check out the Least Common Multiple of 34286 and 34304