What is the Greatest Common Factor of 12300 and 12314?

Greatest common factor (GCF) of 12300 and 12314 is 2.

GCF(12300,12314) = 2

We will now calculate the prime factors of 12300 and 12314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12300 and 12314.

How to find the GCF of 12300 and 12314?

We will first find the prime factorization of 12300 and 12314. After we will calculate the factors of 12300 and 12314 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 12314

Prime factors of 12314 are 2, 47, 131. Prime factorization of 12314 in exponential form is:

12314 = 2¹ × 47¹ × 131¹

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 12314

List of positive integer factors of 12314 that divides 12300 without a remainder.

1, 2, 47, 94, 131, 262, 6157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12300 and 12314. The biggest common factor number is the GCF number.
So the greatest common factor 12300 and 12314 is 2.

Also check out the Least Common Multiple of 12300 and 12314