What is the Greatest Common Factor of 2314 and 2322?

Greatest common factor (GCF) of 2314 and 2322 is 2.

GCF(2314,2322) = 2

We will now calculate the prime factors of 2314 and 2322, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2314 and 2322.

How to find the GCF of 2314 and 2322?

We will first find the prime factorization of 2314 and 2322. After we will calculate the factors of 2314 and 2322 and find the biggest common factor number .

Step-1: Prime Factorization of 2314

Prime factors of 2314 are 2, 13, 89. Prime factorization of 2314 in exponential form is:

2314 = 2¹ × 13¹ × 89¹

Step-2: Prime Factorization of 2322

Prime factors of 2322 are 2, 3, 43. Prime factorization of 2322 in exponential form is:

2322 = 2¹ × 3³ × 43¹

Step-3: Factors of 2314

List of positive integer factors of 2314 that divides 2314 without a remainder.

1, 2, 13, 26, 89, 178, 1157

Step-4: Factors of 2322

List of positive integer factors of 2322 that divides 2314 without a remainder.

1, 2, 3, 6, 9, 18, 27, 43, 54, 86, 129, 258, 387, 774, 1161

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2314 and 2322. The biggest common factor number is the GCF number.
So the greatest common factor 2314 and 2322 is 2.

Also check out the Least Common Multiple of 2314 and 2322