What is the Greatest Common Factor of 12105 and 12114?

Greatest common factor (GCF) of 12105 and 12114 is 9.

GCF(12105,12114) = 9

We will now calculate the prime factors of 12105 and 12114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12105 and 12114.

How to find the GCF of 12105 and 12114?

We will first find the prime factorization of 12105 and 12114. After we will calculate the factors of 12105 and 12114 and find the biggest common factor number .

Step-1: Prime Factorization of 12105

Prime factors of 12105 are 3, 5, 269. Prime factorization of 12105 in exponential form is:

12105 = 3² × 5¹ × 269¹

Step-2: Prime Factorization of 12114

Prime factors of 12114 are 2, 3, 673. Prime factorization of 12114 in exponential form is:

12114 = 2¹ × 3² × 673¹

Step-3: Factors of 12105

List of positive integer factors of 12105 that divides 12105 without a remainder.

1, 3, 5, 9, 15, 45, 269, 807, 1345, 2421, 4035

Step-4: Factors of 12114

List of positive integer factors of 12114 that divides 12105 without a remainder.

1, 2, 3, 6, 9, 18, 673, 1346, 2019, 4038, 6057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12105 and 12114. The biggest common factor number is the GCF number.
So the greatest common factor 12105 and 12114 is 9.

Also check out the Least Common Multiple of 12105 and 12114