What is the Greatest Common Factor of 12582 and 12586?

Greatest common factor (GCF) of 12582 and 12586 is 2.

GCF(12582,12586) = 2

We will now calculate the prime factors of 12582 and 12586, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12582 and 12586.

How to find the GCF of 12582 and 12586?

We will first find the prime factorization of 12582 and 12586. After we will calculate the factors of 12582 and 12586 and find the biggest common factor number .

Step-1: Prime Factorization of 12582

Prime factors of 12582 are 2, 3, 233. Prime factorization of 12582 in exponential form is:

12582 = 2¹ × 3³ × 233¹

Step-2: 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-3: Factors of 12582

List of positive integer factors of 12582 that divides 12582 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 233, 466, 699, 1398, 2097, 4194, 6291

Step-4: Factors of 12586

List of positive integer factors of 12586 that divides 12582 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12582 and 12586. The biggest common factor number is the GCF number.
So the greatest common factor 12582 and 12586 is 2.

Also check out the Least Common Multiple of 12582 and 12586