What is the Greatest Common Factor of 12288 and 12304?

Greatest common factor (GCF) of 12288 and 12304 is 16.

GCF(12288,12304) = 16

We will now calculate the prime factors of 12288 and 12304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12288 and 12304.

How to find the GCF of 12288 and 12304?

We will first find the prime factorization of 12288 and 12304. After we will calculate the factors of 12288 and 12304 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 12304

Prime factors of 12304 are 2, 769. Prime factorization of 12304 in exponential form is:

12304 = 2⁴ × 769¹

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 12304

List of positive integer factors of 12304 that divides 12288 without a remainder.

1, 2, 4, 8, 16, 769, 1538, 3076, 6152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12288 and 12304. The biggest common factor number is the GCF number.
So the greatest common factor 12288 and 12304 is 16.

Also check out the Least Common Multiple of 12288 and 12304