What is the Greatest Common Factor of 14574 and 14589?

Greatest common factor (GCF) of 14574 and 14589 is 3.

GCF(14574,14589) = 3

We will now calculate the prime factors of 14574 and 14589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14574 and 14589.

How to find the GCF of 14574 and 14589?

We will first find the prime factorization of 14574 and 14589. After we will calculate the factors of 14574 and 14589 and find the biggest common factor number .

Step-1: Prime Factorization of 14574

Prime factors of 14574 are 2, 3, 7, 347. Prime factorization of 14574 in exponential form is:

14574 = 2¹ × 3¹ × 7¹ × 347¹

Step-2: Prime Factorization of 14589

Prime factors of 14589 are 3, 1621. Prime factorization of 14589 in exponential form is:

14589 = 3² × 1621¹

Step-3: Factors of 14574

List of positive integer factors of 14574 that divides 14574 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 347, 694, 1041, 2082, 2429, 4858, 7287

Step-4: Factors of 14589

List of positive integer factors of 14589 that divides 14574 without a remainder.

1, 3, 9, 1621, 4863

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14574 and 14589. The biggest common factor number is the GCF number.
So the greatest common factor 14574 and 14589 is 3.

Also check out the Least Common Multiple of 14574 and 14589