What is the Greatest Common Factor of 14586 and 14600?

Greatest common factor (GCF) of 14586 and 14600 is 2.

GCF(14586,14600) = 2

We will now calculate the prime factors of 14586 and 14600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14586 and 14600.

How to find the GCF of 14586 and 14600?

We will first find the prime factorization of 14586 and 14600. After we will calculate the factors of 14586 and 14600 and find the biggest common factor number .

Step-1: Prime Factorization of 14586

Prime factors of 14586 are 2, 3, 11, 13, 17. Prime factorization of 14586 in exponential form is:

14586 = 2¹ × 3¹ × 11¹ × 13¹ × 17¹

Step-2: Prime Factorization of 14600

Prime factors of 14600 are 2, 5, 73. Prime factorization of 14600 in exponential form is:

14600 = 2³ × 5² × 73¹

Step-3: Factors of 14586

List of positive integer factors of 14586 that divides 14586 without a remainder.

1, 2, 3, 6, 11, 13, 17, 22, 26, 33, 34, 39, 51, 66, 78, 102, 143, 187, 221, 286, 374, 429, 442, 561, 663, 858, 1122, 1326, 2431, 4862, 7293

Step-4: Factors of 14600

List of positive integer factors of 14600 that divides 14586 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 73, 100, 146, 200, 292, 365, 584, 730, 1460, 1825, 2920, 3650, 7300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14586 and 14600. The biggest common factor number is the GCF number.
So the greatest common factor 14586 and 14600 is 2.

Also check out the Least Common Multiple of 14586 and 14600