What is the Greatest Common Factor of 2589 and 2600?

Greatest common factor (GCF) of 2589 and 2600 is 1.

GCF(2589,2600) = 1

We will now calculate the prime factors of 2589 and 2600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2589 and 2600.

How to find the GCF of 2589 and 2600?

We will first find the prime factorization of 2589 and 2600. After we will calculate the factors of 2589 and 2600 and find the biggest common factor number .

Step-1: Prime Factorization of 2589

Prime factors of 2589 are 3, 863. Prime factorization of 2589 in exponential form is:

2589 = 3¹ × 863¹

Step-2: Prime Factorization of 2600

Prime factors of 2600 are 2, 5, 13. Prime factorization of 2600 in exponential form is:

2600 = 2³ × 5² × 13¹

Step-3: Factors of 2589

List of positive integer factors of 2589 that divides 2589 without a remainder.

1, 3, 863

Step-4: Factors of 2600

List of positive integer factors of 2600 that divides 2589 without a remainder.

1, 2, 4, 5, 8, 10, 13, 20, 25, 26, 40, 50, 52, 65, 100, 104, 130, 200, 260, 325, 520, 650, 1300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2589 and 2600. The biggest common factor number is the GCF number.
So the greatest common factor 2589 and 2600 is 1.

Also check out the Least Common Multiple of 2589 and 2600