What is the Greatest Common Factor of 12180 and 12200?

Greatest common factor (GCF) of 12180 and 12200 is 20.

GCF(12180,12200) = 20

We will now calculate the prime factors of 12180 and 12200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12180 and 12200.

How to find the GCF of 12180 and 12200?

We will first find the prime factorization of 12180 and 12200. After we will calculate the factors of 12180 and 12200 and find the biggest common factor number .

Step-1: Prime Factorization of 12180

Prime factors of 12180 are 2, 3, 5, 7, 29. Prime factorization of 12180 in exponential form is:

12180 = 2² × 3¹ × 5¹ × 7¹ × 29¹

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 12180

List of positive integer factors of 12180 that divides 12180 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 29, 30, 35, 42, 58, 60, 70, 84, 87, 105, 116, 140, 145, 174, 203, 210, 290, 348, 406, 420, 435, 580, 609, 812, 870, 1015, 1218, 1740, 2030, 2436, 3045, 4060, 6090

Step-4: Factors of 12200

List of positive integer factors of 12200 that divides 12180 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 12180 and 12200. The biggest common factor number is the GCF number.
So the greatest common factor 12180 and 12200 is 20.

Also check out the Least Common Multiple of 12180 and 12200