What is the Greatest Common Factor of 12200 and 12214?

Greatest common factor (GCF) of 12200 and 12214 is 2.

GCF(12200,12214) = 2

We will now calculate the prime factors of 12200 and 12214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12200 and 12214.

How to find the GCF of 12200 and 12214?

We will first find the prime factorization of 12200 and 12214. After we will calculate the factors of 12200 and 12214 and find the biggest common factor number .

Step-1: Prime Factorization of 12200

Prime factors of 12200 are 2, 5, 61. Prime factorization of 12200 in exponential form is:

12200 = 2³ × 5² × 61¹

Step-2: Prime Factorization of 12214

Prime factors of 12214 are 2, 31, 197. Prime factorization of 12214 in exponential form is:

12214 = 2¹ × 31¹ × 197¹

Step-3: Factors of 12200

List of positive integer factors of 12200 that divides 12200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 61, 100, 122, 200, 244, 305, 488, 610, 1220, 1525, 2440, 3050, 6100

Step-4: Factors of 12214

List of positive integer factors of 12214 that divides 12200 without a remainder.

1, 2, 31, 62, 197, 394, 6107

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12200 and 12214. The biggest common factor number is the GCF number.
So the greatest common factor 12200 and 12214 is 2.

Also check out the Least Common Multiple of 12200 and 12214