What is the Greatest Common Factor of 10585 and 10589?

Greatest common factor (GCF) of 10585 and 10589 is 1.

GCF(10585,10589) = 1

We will now calculate the prime factors of 10585 and 10589, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10585 and 10589.

How to find the GCF of 10585 and 10589?

We will first find the prime factorization of 10585 and 10589. After we will calculate the factors of 10585 and 10589 and find the biggest common factor number .

Step-1: Prime Factorization of 10585

Prime factors of 10585 are 5, 29, 73. Prime factorization of 10585 in exponential form is:

10585 = 5¹ × 29¹ × 73¹

Step-2: Prime Factorization of 10589

Prime factors of 10589 are 10589. Prime factorization of 10589 in exponential form is:

10589 = 10589¹

Step-3: Factors of 10585

List of positive integer factors of 10585 that divides 10585 without a remainder.

1, 5, 29, 73, 145, 365, 2117

Step-4: Factors of 10589

List of positive integer factors of 10589 that divides 10585 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10585 and 10589. The biggest common factor number is the GCF number.
So the greatest common factor 10585 and 10589 is 1.

Also check out the Least Common Multiple of 10585 and 10589