What is the Greatest Common Factor of 12075 and 12084?

Greatest common factor (GCF) of 12075 and 12084 is 3.

GCF(12075,12084) = 3

We will now calculate the prime factors of 12075 and 12084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12075 and 12084.

How to find the GCF of 12075 and 12084?

We will first find the prime factorization of 12075 and 12084. After we will calculate the factors of 12075 and 12084 and find the biggest common factor number .

Step-1: Prime Factorization of 12075

Prime factors of 12075 are 3, 5, 7, 23. Prime factorization of 12075 in exponential form is:

12075 = 3¹ × 5² × 7¹ × 23¹

Step-2: 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-3: Factors of 12075

List of positive integer factors of 12075 that divides 12075 without a remainder.

1, 3, 5, 7, 15, 21, 23, 25, 35, 69, 75, 105, 115, 161, 175, 345, 483, 525, 575, 805, 1725, 2415, 4025

Step-4: Factors of 12084

List of positive integer factors of 12084 that divides 12075 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12075 and 12084. The biggest common factor number is the GCF number.
So the greatest common factor 12075 and 12084 is 3.

Also check out the Least Common Multiple of 12075 and 12084