What is the Greatest Common Factor of 22304 and 22321?

Greatest common factor (GCF) of 22304 and 22321 is 17.

GCF(22304,22321) = 17

We will now calculate the prime factors of 22304 and 22321, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22304 and 22321.

How to find the GCF of 22304 and 22321?

We will first find the prime factorization of 22304 and 22321. After we will calculate the factors of 22304 and 22321 and find the biggest common factor number .

Step-1: Prime Factorization of 22304

Prime factors of 22304 are 2, 17, 41. Prime factorization of 22304 in exponential form is:

22304 = 2⁵ × 17¹ × 41¹

Step-2: Prime Factorization of 22321

Prime factors of 22321 are 13, 17, 101. Prime factorization of 22321 in exponential form is:

22321 = 13¹ × 17¹ × 101¹

Step-3: Factors of 22304

List of positive integer factors of 22304 that divides 22304 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 41, 68, 82, 136, 164, 272, 328, 544, 656, 697, 1312, 1394, 2788, 5576, 11152

Step-4: Factors of 22321

List of positive integer factors of 22321 that divides 22304 without a remainder.

1, 13, 17, 101, 221, 1313, 1717

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22304 and 22321. The biggest common factor number is the GCF number.
So the greatest common factor 22304 and 22321 is 17.

Also check out the Least Common Multiple of 22304 and 22321