What is the Greatest Common Factor of 12123 and 12138?

Greatest common factor (GCF) of 12123 and 12138 is 3.

GCF(12123,12138) = 3

We will now calculate the prime factors of 12123 and 12138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12123 and 12138.

How to find the GCF of 12123 and 12138?

We will first find the prime factorization of 12123 and 12138. After we will calculate the factors of 12123 and 12138 and find the biggest common factor number .

Step-1: Prime Factorization of 12123

Prime factors of 12123 are 3, 449. Prime factorization of 12123 in exponential form is:

12123 = 3³ × 449¹

Step-2: Prime Factorization of 12138

Prime factors of 12138 are 2, 3, 7, 17. Prime factorization of 12138 in exponential form is:

12138 = 2¹ × 3¹ × 7¹ × 17²

Step-3: Factors of 12123

List of positive integer factors of 12123 that divides 12123 without a remainder.

1, 3, 9, 27, 449, 1347, 4041

Step-4: Factors of 12138

List of positive integer factors of 12138 that divides 12123 without a remainder.

1, 2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 289, 357, 578, 714, 867, 1734, 2023, 4046, 6069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12123 and 12138. The biggest common factor number is the GCF number.
So the greatest common factor 12123 and 12138 is 3.

Also check out the Least Common Multiple of 12123 and 12138