What is the Greatest Common Factor of 6589 and 6600?

Greatest common factor (GCF) of 6589 and 6600 is 11.

GCF(6589,6600) = 11

We will now calculate the prime factors of 6589 and 6600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6589 and 6600.

How to find the GCF of 6589 and 6600?

We will first find the prime factorization of 6589 and 6600. After we will calculate the factors of 6589 and 6600 and find the biggest common factor number .

Step-1: Prime Factorization of 6589

Prime factors of 6589 are 11, 599. Prime factorization of 6589 in exponential form is:

6589 = 11¹ × 599¹

Step-2: Prime Factorization of 6600

Prime factors of 6600 are 2, 3, 5, 11. Prime factorization of 6600 in exponential form is:

6600 = 2³ × 3¹ × 5² × 11¹

Step-3: Factors of 6589

List of positive integer factors of 6589 that divides 6589 without a remainder.

1, 11, 599

Step-4: Factors of 6600

List of positive integer factors of 6600 that divides 6589 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 25, 30, 33, 40, 44, 50, 55, 60, 66, 75, 88, 100, 110, 120, 132, 150, 165, 200, 220, 264, 275, 300, 330, 440, 550, 600, 660, 825, 1100, 1320, 1650, 2200, 3300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6589 and 6600. The biggest common factor number is the GCF number.
So the greatest common factor 6589 and 6600 is 11.

Also check out the Least Common Multiple of 6589 and 6600