What is the Greatest Common Factor of 12200 and 12208?

Greatest common factor (GCF) of 12200 and 12208 is 8.

GCF(12200,12208) = 8

We will now calculate the prime factors of 12200 and 12208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12200 and 12208.

How to find the GCF of 12200 and 12208?

We will first find the prime factorization of 12200 and 12208. After we will calculate the factors of 12200 and 12208 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 12208

Prime factors of 12208 are 2, 7, 109. Prime factorization of 12208 in exponential form is:

12208 = 2⁴ × 7¹ × 109¹

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 12208

List of positive integer factors of 12208 that divides 12200 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 109, 112, 218, 436, 763, 872, 1526, 1744, 3052, 6104

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12200 and 12208. The biggest common factor number is the GCF number.
So the greatest common factor 12200 and 12208 is 8.

Also check out the Least Common Multiple of 12200 and 12208