What is the Greatest Common Factor of 12208 and 12224?

Greatest common factor (GCF) of 12208 and 12224 is 16.

GCF(12208,12224) = 16

We will now calculate the prime factors of 12208 and 12224, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12208 and 12224.

How to find the GCF of 12208 and 12224?

We will first find the prime factorization of 12208 and 12224. After we will calculate the factors of 12208 and 12224 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12224

Prime factors of 12224 are 2, 191. Prime factorization of 12224 in exponential form is:

12224 = 2⁶ × 191¹

Step-3: Factors of 12208

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

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

Step-4: Factors of 12224

List of positive integer factors of 12224 that divides 12208 without a remainder.

1, 2, 4, 8, 16, 32, 64, 191, 382, 764, 1528, 3056, 6112

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12208 and 12224. The biggest common factor number is the GCF number.
So the greatest common factor 12208 and 12224 is 16.

Also check out the Least Common Multiple of 12208 and 12224