What is the Greatest Common Factor of 12075 and 12090?

Greatest common factor (GCF) of 12075 and 12090 is 15.

GCF(12075,12090) = 15

We will now calculate the prime factors of 12075 and 12090, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12075 and 12090.

How to find the GCF of 12075 and 12090?

We will first find the prime factorization of 12075 and 12090. After we will calculate the factors of 12075 and 12090 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 12090

Prime factors of 12090 are 2, 3, 5, 13, 31. Prime factorization of 12090 in exponential form is:

12090 = 2¹ × 3¹ × 5¹ × 13¹ × 31¹

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 12090

List of positive integer factors of 12090 that divides 12075 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 31, 39, 62, 65, 78, 93, 130, 155, 186, 195, 310, 390, 403, 465, 806, 930, 1209, 2015, 2418, 4030, 6045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12075 and 12090. The biggest common factor number is the GCF number.
So the greatest common factor 12075 and 12090 is 15.

Also check out the Least Common Multiple of 12075 and 12090