What is the Greatest Common Factor of 12288 and 12296?

Greatest common factor (GCF) of 12288 and 12296 is 8.

GCF(12288,12296) = 8

We will now calculate the prime factors of 12288 and 12296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12288 and 12296.

How to find the GCF of 12288 and 12296?

We will first find the prime factorization of 12288 and 12296. After we will calculate the factors of 12288 and 12296 and find the biggest common factor number .

Step-1: Prime Factorization of 12288

Prime factors of 12288 are 2, 3. Prime factorization of 12288 in exponential form is:

12288 = 2¹² × 3¹

Step-2: Prime Factorization of 12296

Prime factors of 12296 are 2, 29, 53. Prime factorization of 12296 in exponential form is:

12296 = 2³ × 29¹ × 53¹

Step-3: Factors of 12288

List of positive integer factors of 12288 that divides 12288 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144

Step-4: Factors of 12296

List of positive integer factors of 12296 that divides 12288 without a remainder.

1, 2, 4, 8, 29, 53, 58, 106, 116, 212, 232, 424, 1537, 3074, 6148

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12288 and 12296. The biggest common factor number is the GCF number.
So the greatest common factor 12288 and 12296 is 8.

Also check out the Least Common Multiple of 12288 and 12296