What is the Greatest Common Factor of 12586 and 12593?

Greatest common factor (GCF) of 12586 and 12593 is 7.

GCF(12586,12593) = 7

We will now calculate the prime factors of 12586 and 12593, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12586 and 12593.

How to find the GCF of 12586 and 12593?

We will first find the prime factorization of 12586 and 12593. After we will calculate the factors of 12586 and 12593 and find the biggest common factor number .

Step-1: Prime Factorization of 12586

Prime factors of 12586 are 2, 7, 29, 31. Prime factorization of 12586 in exponential form is:

12586 = 2¹ × 7¹ × 29¹ × 31¹

Step-2: Prime Factorization of 12593

Prime factors of 12593 are 7, 257. Prime factorization of 12593 in exponential form is:

12593 = 7² × 257¹

Step-3: Factors of 12586

List of positive integer factors of 12586 that divides 12586 without a remainder.

1, 2, 7, 14, 29, 31, 58, 62, 203, 217, 406, 434, 899, 1798, 6293

Step-4: Factors of 12593

List of positive integer factors of 12593 that divides 12586 without a remainder.

1, 7, 49, 257, 1799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12586 and 12593. The biggest common factor number is the GCF number.
So the greatest common factor 12586 and 12593 is 7.

Also check out the Least Common Multiple of 12586 and 12593