What is the Greatest Common Factor of 12300 and 12317?

Greatest common factor (GCF) of 12300 and 12317 is 1.

GCF(12300,12317) = 1

We will now calculate the prime factors of 12300 and 12317, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12300 and 12317.

How to find the GCF of 12300 and 12317?

We will first find the prime factorization of 12300 and 12317. After we will calculate the factors of 12300 and 12317 and find the biggest common factor number .

Step-1: Prime Factorization of 12300

Prime factors of 12300 are 2, 3, 5, 41. Prime factorization of 12300 in exponential form is:

12300 = 2² × 3¹ × 5² × 41¹

Step-2: Prime Factorization of 12317

Prime factors of 12317 are 109, 113. Prime factorization of 12317 in exponential form is:

12317 = 109¹ × 113¹

Step-3: Factors of 12300

List of positive integer factors of 12300 that divides 12300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 41, 50, 60, 75, 82, 100, 123, 150, 164, 205, 246, 300, 410, 492, 615, 820, 1025, 1230, 2050, 2460, 3075, 4100, 6150

Step-4: Factors of 12317

List of positive integer factors of 12317 that divides 12300 without a remainder.

1, 109, 113

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12300 and 12317. The biggest common factor number is the GCF number.
So the greatest common factor 12300 and 12317 is 1.

Also check out the Least Common Multiple of 12300 and 12317