What is the Greatest Common Factor of 2289 and 2304?

Greatest common factor (GCF) of 2289 and 2304 is 3.

GCF(2289,2304) = 3

We will now calculate the prime factors of 2289 and 2304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2289 and 2304.

How to find the GCF of 2289 and 2304?

We will first find the prime factorization of 2289 and 2304. After we will calculate the factors of 2289 and 2304 and find the biggest common factor number .

Step-1: Prime Factorization of 2289

Prime factors of 2289 are 3, 7, 109. Prime factorization of 2289 in exponential form is:

2289 = 3¹ × 7¹ × 109¹

Step-2: Prime Factorization of 2304

Prime factors of 2304 are 2, 3. Prime factorization of 2304 in exponential form is:

2304 = 2⁸ × 3²

Step-3: Factors of 2289

List of positive integer factors of 2289 that divides 2289 without a remainder.

1, 3, 7, 21, 109, 327, 763

Step-4: Factors of 2304

List of positive integer factors of 2304 that divides 2289 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 256, 288, 384, 576, 768, 1152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2289 and 2304. The biggest common factor number is the GCF number.
So the greatest common factor 2289 and 2304 is 3.

Also check out the Least Common Multiple of 2289 and 2304