What is the Greatest Common Factor of 2299 and 2312?

Greatest common factor (GCF) of 2299 and 2312 is 1.

GCF(2299,2312) = 1

We will now calculate the prime factors of 2299 and 2312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2299 and 2312.

How to find the GCF of 2299 and 2312?

We will first find the prime factorization of 2299 and 2312. After we will calculate the factors of 2299 and 2312 and find the biggest common factor number .

Step-1: Prime Factorization of 2299

Prime factors of 2299 are 11, 19. Prime factorization of 2299 in exponential form is:

2299 = 11² × 19¹

Step-2: Prime Factorization of 2312

Prime factors of 2312 are 2, 17. Prime factorization of 2312 in exponential form is:

2312 = 2³ × 17²

Step-3: Factors of 2299

List of positive integer factors of 2299 that divides 2299 without a remainder.

1, 11, 19, 121, 209

Step-4: Factors of 2312

List of positive integer factors of 2312 that divides 2299 without a remainder.

1, 2, 4, 8, 17, 34, 68, 136, 289, 578, 1156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2299 and 2312. The biggest common factor number is the GCF number.
So the greatest common factor 2299 and 2312 is 1.

Also check out the Least Common Multiple of 2299 and 2312