What is the Greatest Common Factor of 12714 and 12723?

Greatest common factor (GCF) of 12714 and 12723 is 3.

GCF(12714,12723) = 3

We will now calculate the prime factors of 12714 and 12723, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12714 and 12723.

How to find the GCF of 12714 and 12723?

We will first find the prime factorization of 12714 and 12723. After we will calculate the factors of 12714 and 12723 and find the biggest common factor number .

Step-1: Prime Factorization of 12714

Prime factors of 12714 are 2, 3, 13, 163. Prime factorization of 12714 in exponential form is:

12714 = 2¹ × 3¹ × 13¹ × 163¹

Step-2: Prime Factorization of 12723

Prime factors of 12723 are 3, 4241. Prime factorization of 12723 in exponential form is:

12723 = 3¹ × 4241¹

Step-3: Factors of 12714

List of positive integer factors of 12714 that divides 12714 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 163, 326, 489, 978, 2119, 4238, 6357

Step-4: Factors of 12723

List of positive integer factors of 12723 that divides 12714 without a remainder.

1, 3, 4241

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12714 and 12723. The biggest common factor number is the GCF number.
So the greatest common factor 12714 and 12723 is 3.

Also check out the Least Common Multiple of 12714 and 12723