What is the Greatest Common Factor of 12096 and 12105?

Greatest common factor (GCF) of 12096 and 12105 is 9.

GCF(12096,12105) = 9

We will now calculate the prime factors of 12096 and 12105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12096 and 12105.

How to find the GCF of 12096 and 12105?

We will first find the prime factorization of 12096 and 12105. After we will calculate the factors of 12096 and 12105 and find the biggest common factor number .

Step-1: Prime Factorization of 12096

Prime factors of 12096 are 2, 3, 7. Prime factorization of 12096 in exponential form is:

12096 = 2⁶ × 3³ × 7¹

Step-2: Prime Factorization of 12105

Prime factors of 12105 are 3, 5, 269. Prime factorization of 12105 in exponential form is:

12105 = 3² × 5¹ × 269¹

Step-3: Factors of 12096

List of positive integer factors of 12096 that divides 12096 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 64, 72, 84, 96, 108, 112, 126, 144, 168, 189, 192, 216, 224, 252, 288, 336, 378, 432, 448, 504, 576, 672, 756, 864, 1008, 1344, 1512, 1728, 2016, 3024, 4032, 6048

Step-4: Factors of 12105

List of positive integer factors of 12105 that divides 12096 without a remainder.

1, 3, 5, 9, 15, 45, 269, 807, 1345, 2421, 4035

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12096 and 12105. The biggest common factor number is the GCF number.
So the greatest common factor 12096 and 12105 is 9.

Also check out the Least Common Multiple of 12096 and 12105