What is the Greatest Common Factor of 12186 and 12200?

Greatest common factor (GCF) of 12186 and 12200 is 2.

GCF(12186,12200) = 2

We will now calculate the prime factors of 12186 and 12200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12186 and 12200.

How to find the GCF of 12186 and 12200?

We will first find the prime factorization of 12186 and 12200. After we will calculate the factors of 12186 and 12200 and find the biggest common factor number .

Step-1: Prime Factorization of 12186

Prime factors of 12186 are 2, 3, 677. Prime factorization of 12186 in exponential form is:

12186 = 2¹ × 3² × 677¹

Step-2: 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-3: Factors of 12186

List of positive integer factors of 12186 that divides 12186 without a remainder.

1, 2, 3, 6, 9, 18, 677, 1354, 2031, 4062, 6093

Step-4: Factors of 12200

List of positive integer factors of 12200 that divides 12186 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12186 and 12200. The biggest common factor number is the GCF number.
So the greatest common factor 12186 and 12200 is 2.

Also check out the Least Common Multiple of 12186 and 12200