What is the Greatest Common Factor of 82304 and 82322?

Greatest common factor (GCF) of 82304 and 82322 is 2.

GCF(82304,82322) = 2

We will now calculate the prime factors of 82304 and 82322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82304 and 82322.

How to find the GCF of 82304 and 82322?

We will first find the prime factorization of 82304 and 82322. After we will calculate the factors of 82304 and 82322 and find the biggest common factor number .

Step-1: Prime Factorization of 82304

Prime factors of 82304 are 2, 643. Prime factorization of 82304 in exponential form is:

82304 = 2⁷ × 643¹

Step-2: Prime Factorization of 82322

Prime factors of 82322 are 2, 41161. Prime factorization of 82322 in exponential form is:

82322 = 2¹ × 41161¹

Step-3: Factors of 82304

List of positive integer factors of 82304 that divides 82304 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 643, 1286, 2572, 5144, 10288, 20576, 41152

Step-4: Factors of 82322

List of positive integer factors of 82322 that divides 82304 without a remainder.

1, 2, 41161

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82304 and 82322. The biggest common factor number is the GCF number.
So the greatest common factor 82304 and 82322 is 2.

Also check out the Least Common Multiple of 82304 and 82322