What is the Greatest Common Factor of 12586 and 12590?

Greatest common factor (GCF) of 12586 and 12590 is 2.

GCF(12586,12590) = 2

We will now calculate the prime factors of 12586 and 12590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12586 and 12590.

How to find the GCF of 12586 and 12590?

We will first find the prime factorization of 12586 and 12590. After we will calculate the factors of 12586 and 12590 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 12590

Prime factors of 12590 are 2, 5, 1259. Prime factorization of 12590 in exponential form is:

12590 = 2¹ × 5¹ × 1259¹

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 12590

List of positive integer factors of 12590 that divides 12586 without a remainder.

1, 2, 5, 10, 1259, 2518, 6295

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12586 and 12590. The biggest common factor number is the GCF number.
So the greatest common factor 12586 and 12590 is 2.

Also check out the Least Common Multiple of 12586 and 12590