What is the Greatest Common Factor of 12397 and 12414?

Greatest common factor (GCF) of 12397 and 12414 is 1.

GCF(12397,12414) = 1

We will now calculate the prime factors of 12397 and 12414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12397 and 12414.

How to find the GCF of 12397 and 12414?

We will first find the prime factorization of 12397 and 12414. After we will calculate the factors of 12397 and 12414 and find the biggest common factor number .

Step-1: Prime Factorization of 12397

Prime factors of 12397 are 7, 11, 23. Prime factorization of 12397 in exponential form is:

12397 = 7² × 11¹ × 23¹

Step-2: Prime Factorization of 12414

Prime factors of 12414 are 2, 3, 2069. Prime factorization of 12414 in exponential form is:

12414 = 2¹ × 3¹ × 2069¹

Step-3: Factors of 12397

List of positive integer factors of 12397 that divides 12397 without a remainder.

1, 7, 11, 23, 49, 77, 161, 253, 539, 1127, 1771

Step-4: Factors of 12414

List of positive integer factors of 12414 that divides 12397 without a remainder.

1, 2, 3, 6, 2069, 4138, 6207

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12397 and 12414. The biggest common factor number is the GCF number.
So the greatest common factor 12397 and 12414 is 1.

Also check out the Least Common Multiple of 12397 and 12414