What is the Greatest Common Factor of 12288 and 12300?

Greatest common factor (GCF) of 12288 and 12300 is 12.

GCF(12288,12300) = 12

We will now calculate the prime factors of 12288 and 12300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12288 and 12300.

How to find the GCF of 12288 and 12300?

We will first find the prime factorization of 12288 and 12300. After we will calculate the factors of 12288 and 12300 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 12300

Prime factors of 12300 are 2, 3, 5, 41. Prime factorization of 12300 in exponential form is:

12300 = 2² × 3¹ × 5² × 41¹

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 12300

List of positive integer factors of 12300 that divides 12288 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 41, 50, 60, 75, 82, 100, 123, 150, 164, 205, 246, 300, 410, 492, 615, 820, 1025, 1230, 2050, 2460, 3075, 4100, 6150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12288 and 12300. The biggest common factor number is the GCF number.
So the greatest common factor 12288 and 12300 is 12.

Also check out the Least Common Multiple of 12288 and 12300