What is the Greatest Common Factor of 22289 and 22304?

Greatest common factor (GCF) of 22289 and 22304 is 1.

GCF(22289,22304) = 1

We will now calculate the prime factors of 22289 and 22304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22289 and 22304.

How to find the GCF of 22289 and 22304?

We will first find the prime factorization of 22289 and 22304. After we will calculate the factors of 22289 and 22304 and find the biggest common factor number .

Step-1: Prime Factorization of 22289

Prime factors of 22289 are 31, 719. Prime factorization of 22289 in exponential form is:

22289 = 31¹ × 719¹

Step-2: 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-3: Factors of 22289

List of positive integer factors of 22289 that divides 22289 without a remainder.

1, 31, 719

Step-4: Factors of 22304

List of positive integer factors of 22304 that divides 22289 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22289 and 22304. The biggest common factor number is the GCF number.
So the greatest common factor 22289 and 22304 is 1.

Also check out the Least Common Multiple of 22289 and 22304