What is the Greatest Common Factor of 2300 and 2310?

Greatest common factor (GCF) of 2300 and 2310 is 10.

GCF(2300,2310) = 10

We will now calculate the prime factors of 2300 and 2310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2300 and 2310.

How to find the GCF of 2300 and 2310?

We will first find the prime factorization of 2300 and 2310. After we will calculate the factors of 2300 and 2310 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 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 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 2310

List of positive integer factors of 2310 that divides 2300 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 2300 and 2310. The biggest common factor number is the GCF number.
So the greatest common factor 2300 and 2310 is 10.

Also check out the Least Common Multiple of 2300 and 2310