What is the Greatest Common Factor of 14569 and 14586?

Greatest common factor (GCF) of 14569 and 14586 is 17.

GCF(14569,14586) = 17

We will now calculate the prime factors of 14569 and 14586, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14569 and 14586.

How to find the GCF of 14569 and 14586?

We will first find the prime factorization of 14569 and 14586. After we will calculate the factors of 14569 and 14586 and find the biggest common factor number .

Step-1: Prime Factorization of 14569

Prime factors of 14569 are 17, 857. Prime factorization of 14569 in exponential form is:

14569 = 17¹ × 857¹

Step-2: 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-3: Factors of 14569

List of positive integer factors of 14569 that divides 14569 without a remainder.

1, 17, 857

Step-4: Factors of 14586

List of positive integer factors of 14586 that divides 14569 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14569 and 14586. The biggest common factor number is the GCF number.
So the greatest common factor 14569 and 14586 is 17.

Also check out the Least Common Multiple of 14569 and 14586