What is the Greatest Common Factor of 14569 and 14580?

Greatest common factor (GCF) of 14569 and 14580 is 1.

GCF(14569,14580) = 1

We will now calculate the prime factors of 14569 and 14580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14569 and 14580.

How to find the GCF of 14569 and 14580?

We will first find the prime factorization of 14569 and 14580. After we will calculate the factors of 14569 and 14580 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 14580

Prime factors of 14580 are 2, 3, 5. Prime factorization of 14580 in exponential form is:

14580 = 2² × 3⁶ × 5¹

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 14580

List of positive integer factors of 14580 that divides 14569 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 243, 270, 324, 405, 486, 540, 729, 810, 972, 1215, 1458, 1620, 2430, 2916, 3645, 4860, 7290

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14569 and 14580. The biggest common factor number is the GCF number.
So the greatest common factor 14569 and 14580 is 1.

Also check out the Least Common Multiple of 14569 and 14580