What is the Greatest Common Factor of 2296 and 2310?

Greatest common factor (GCF) of 2296 and 2310 is 14.

GCF(2296,2310) = 14

We will now calculate the prime factors of 2296 and 2310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2296 and 2310.

How to find the GCF of 2296 and 2310?

We will first find the prime factorization of 2296 and 2310. After we will calculate the factors of 2296 and 2310 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 2310

Prime factors of 2310 are 2, 3, 5, 7, 11. Prime factorization of 2310 in exponential form is:

2310 = 2¹ × 3¹ × 5¹ × 7¹ × 11¹

Step-3: Factors of 2296

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

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

Step-4: Factors of 2310

List of positive integer factors of 2310 that divides 2296 without a remainder.

1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2296 and 2310. The biggest common factor number is the GCF number.
So the greatest common factor 2296 and 2310 is 14.

Also check out the Least Common Multiple of 2296 and 2310