What is the Greatest Common Factor of 2289 and 2296?

Greatest common factor (GCF) of 2289 and 2296 is 7.

GCF(2289,2296) = 7

We will now calculate the prime factors of 2289 and 2296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2289 and 2296.

How to find the GCF of 2289 and 2296?

We will first find the prime factorization of 2289 and 2296. After we will calculate the factors of 2289 and 2296 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 2296

Prime factors of 2296 are 2, 7, 41. Prime factorization of 2296 in exponential form is:

2296 = 2³ × 7¹ × 41¹

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 2296

List of positive integer factors of 2296 that divides 2289 without a remainder.

1, 2, 4, 7, 8, 14, 28, 41, 56, 82, 164, 287, 328, 574, 1148

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2289 and 2296. The biggest common factor number is the GCF number.
So the greatest common factor 2289 and 2296 is 7.

Also check out the Least Common Multiple of 2289 and 2296