What is the Greatest Common Factor of 12096 and 12100?

Greatest common factor (GCF) of 12096 and 12100 is 4.

GCF(12096,12100) = 4

We will now calculate the prime factors of 12096 and 12100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12096 and 12100.

How to find the GCF of 12096 and 12100?

We will first find the prime factorization of 12096 and 12100. After we will calculate the factors of 12096 and 12100 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 12100

Prime factors of 12100 are 2, 5, 11. Prime factorization of 12100 in exponential form is:

12100 = 2² × 5² × 11²

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 12100

List of positive integer factors of 12100 that divides 12096 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 121, 220, 242, 275, 484, 550, 605, 1100, 1210, 2420, 3025, 6050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12096 and 12100. The biggest common factor number is the GCF number.
So the greatest common factor 12096 and 12100 is 4.

Also check out the Least Common Multiple of 12096 and 12100