What is the Greatest Common Factor of 57585 and 57600?

Greatest common factor (GCF) of 57585 and 57600 is 15.

GCF(57585,57600) = 15

We will now calculate the prime factors of 57585 and 57600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 57585 and 57600.

How to find the GCF of 57585 and 57600?

We will first find the prime factorization of 57585 and 57600. After we will calculate the factors of 57585 and 57600 and find the biggest common factor number .

Step-1: Prime Factorization of 57585

Prime factors of 57585 are 3, 5, 11, 349. Prime factorization of 57585 in exponential form is:

57585 = 3¹ × 5¹ × 11¹ × 349¹

Step-2: Prime Factorization of 57600

Prime factors of 57600 are 2, 3, 5. Prime factorization of 57600 in exponential form is:

57600 = 2⁸ × 3² × 5²

Step-3: Factors of 57585

List of positive integer factors of 57585 that divides 57585 without a remainder.

1, 3, 5, 11, 15, 33, 55, 165, 349, 1047, 1745, 3839, 5235, 11517, 19195

Step-4: Factors of 57600

List of positive integer factors of 57600 that divides 57585 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 256, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 768, 800, 900, 960, 1152, 1200, 1280, 1440, 1600, 1800, 1920, 2304, 2400, 2880, 3200, 3600, 3840, 4800, 5760, 6400, 7200, 9600, 11520, 14400, 19200, 28800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 57585 and 57600. The biggest common factor number is the GCF number.
So the greatest common factor 57585 and 57600 is 15.

Also check out the Least Common Multiple of 57585 and 57600