What is the Greatest Common Factor of 12084 and 12096?

Greatest common factor (GCF) of 12084 and 12096 is 12.

GCF(12084,12096) = 12

We will now calculate the prime factors of 12084 and 12096, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12084 and 12096.

How to find the GCF of 12084 and 12096?

We will first find the prime factorization of 12084 and 12096. After we will calculate the factors of 12084 and 12096 and find the biggest common factor number .

Step-1: Prime Factorization of 12084

Prime factors of 12084 are 2, 3, 19, 53. Prime factorization of 12084 in exponential form is:

12084 = 2² × 3¹ × 19¹ × 53¹

Step-2: 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-3: Factors of 12084

List of positive integer factors of 12084 that divides 12084 without a remainder.

1, 2, 3, 4, 6, 12, 19, 38, 53, 57, 76, 106, 114, 159, 212, 228, 318, 636, 1007, 2014, 3021, 4028, 6042

Step-4: Factors of 12096

List of positive integer factors of 12096 that divides 12084 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12084 and 12096. The biggest common factor number is the GCF number.
So the greatest common factor 12084 and 12096 is 12.

Also check out the Least Common Multiple of 12084 and 12096