What is the Greatest Common Factor of 12586 and 12600?

Greatest common factor (GCF) of 12586 and 12600 is 14.

GCF(12586,12600) = 14

We will now calculate the prime factors of 12586 and 12600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12586 and 12600.

How to find the GCF of 12586 and 12600?

We will first find the prime factorization of 12586 and 12600. After we will calculate the factors of 12586 and 12600 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 12600

Prime factors of 12600 are 2, 3, 5, 7. Prime factorization of 12600 in exponential form is:

12600 = 2³ × 3² × 5² × 7¹

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 12600

List of positive integer factors of 12600 that divides 12586 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 50, 56, 60, 63, 70, 72, 75, 84, 90, 100, 105, 120, 126, 140, 150, 168, 175, 180, 200, 210, 225, 252, 280, 300, 315, 350, 360, 420, 450, 504, 525, 600, 630, 700, 840, 900, 1050, 1260, 1400, 1575, 1800, 2100, 2520, 3150, 4200, 6300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12586 and 12600. The biggest common factor number is the GCF number.
So the greatest common factor 12586 and 12600 is 14.

Also check out the Least Common Multiple of 12586 and 12600