What is the Greatest Common Factor of 2300 and 2314?

Greatest common factor (GCF) of 2300 and 2314 is 2.

GCF(2300,2314) = 2

We will now calculate the prime factors of 2300 and 2314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2300 and 2314.

How to find the GCF of 2300 and 2314?

We will first find the prime factorization of 2300 and 2314. After we will calculate the factors of 2300 and 2314 and find the biggest common factor number .

Step-1: Prime Factorization of 2300

Prime factors of 2300 are 2, 5, 23. Prime factorization of 2300 in exponential form is:

2300 = 2² × 5² × 23¹

Step-2: 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-3: Factors of 2300

List of positive integer factors of 2300 that divides 2300 without a remainder.

1, 2, 4, 5, 10, 20, 23, 25, 46, 50, 92, 100, 115, 230, 460, 575, 1150

Step-4: Factors of 2314

List of positive integer factors of 2314 that divides 2300 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2300 and 2314. The biggest common factor number is the GCF number.
So the greatest common factor 2300 and 2314 is 2.

Also check out the Least Common Multiple of 2300 and 2314