What is the Greatest Common Factor of 12069 and 12075?

Greatest common factor (GCF) of 12069 and 12075 is 3.

GCF(12069,12075) = 3

We will now calculate the prime factors of 12069 and 12075, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12069 and 12075.

How to find the GCF of 12069 and 12075?

We will first find the prime factorization of 12069 and 12075. After we will calculate the factors of 12069 and 12075 and find the biggest common factor number .

Step-1: Prime Factorization of 12069

Prime factors of 12069 are 3, 149. Prime factorization of 12069 in exponential form is:

12069 = 3⁴ × 149¹

Step-2: 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-3: Factors of 12069

List of positive integer factors of 12069 that divides 12069 without a remainder.

1, 3, 9, 27, 81, 149, 447, 1341, 4023

Step-4: Factors of 12075

List of positive integer factors of 12075 that divides 12069 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12069 and 12075. The biggest common factor number is the GCF number.
So the greatest common factor 12069 and 12075 is 3.

Also check out the Least Common Multiple of 12069 and 12075