What is the Greatest Common Factor of 12805 and 12814?

Greatest common factor (GCF) of 12805 and 12814 is 1.

GCF(12805,12814) = 1

We will now calculate the prime factors of 12805 and 12814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12805 and 12814.

How to find the GCF of 12805 and 12814?

We will first find the prime factorization of 12805 and 12814. After we will calculate the factors of 12805 and 12814 and find the biggest common factor number .

Step-1: Prime Factorization of 12805

Prime factors of 12805 are 5, 13, 197. Prime factorization of 12805 in exponential form is:

12805 = 5¹ × 13¹ × 197¹

Step-2: Prime Factorization of 12814

Prime factors of 12814 are 2, 43, 149. Prime factorization of 12814 in exponential form is:

12814 = 2¹ × 43¹ × 149¹

Step-3: Factors of 12805

List of positive integer factors of 12805 that divides 12805 without a remainder.

1, 5, 13, 65, 197, 985, 2561

Step-4: Factors of 12814

List of positive integer factors of 12814 that divides 12805 without a remainder.

1, 2, 43, 86, 149, 298, 6407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12805 and 12814. The biggest common factor number is the GCF number.
So the greatest common factor 12805 and 12814 is 1.

Also check out the Least Common Multiple of 12805 and 12814