What is the Greatest Common Factor of 17589 and 17600?

Greatest common factor (GCF) of 17589 and 17600 is 11.

GCF(17589,17600) = 11

We will now calculate the prime factors of 17589 and 17600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17589 and 17600.

How to find the GCF of 17589 and 17600?

We will first find the prime factorization of 17589 and 17600. After we will calculate the factors of 17589 and 17600 and find the biggest common factor number .

Step-1: Prime Factorization of 17589

Prime factors of 17589 are 3, 11, 13, 41. Prime factorization of 17589 in exponential form is:

17589 = 3¹ × 11¹ × 13¹ × 41¹

Step-2: Prime Factorization of 17600

Prime factors of 17600 are 2, 5, 11. Prime factorization of 17600 in exponential form is:

17600 = 2⁶ × 5² × 11¹

Step-3: Factors of 17589

List of positive integer factors of 17589 that divides 17589 without a remainder.

1, 3, 11, 13, 33, 39, 41, 123, 143, 429, 451, 533, 1353, 1599, 5863

Step-4: Factors of 17600

List of positive integer factors of 17600 that divides 17589 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 64, 80, 88, 100, 110, 160, 176, 200, 220, 275, 320, 352, 400, 440, 550, 704, 800, 880, 1100, 1600, 1760, 2200, 3520, 4400, 8800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17589 and 17600. The biggest common factor number is the GCF number.
So the greatest common factor 17589 and 17600 is 11.

Also check out the Least Common Multiple of 17589 and 17600