What is the Greatest Common Factor of 75585 and 75600?

Greatest common factor (GCF) of 75585 and 75600 is 15.

GCF(75585,75600) = 15

We will now calculate the prime factors of 75585 and 75600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75585 and 75600.

How to find the GCF of 75585 and 75600?

We will first find the prime factorization of 75585 and 75600. After we will calculate the factors of 75585 and 75600 and find the biggest common factor number .

Step-1: Prime Factorization of 75585

Prime factors of 75585 are 3, 5, 5039. Prime factorization of 75585 in exponential form is:

75585 = 3¹ × 5¹ × 5039¹

Step-2: Prime Factorization of 75600

Prime factors of 75600 are 2, 3, 5, 7. Prime factorization of 75600 in exponential form is:

75600 = 2⁴ × 3³ × 5² × 7¹

Step-3: Factors of 75585

List of positive integer factors of 75585 that divides 75585 without a remainder.

1, 3, 5, 15, 5039, 15117, 25195

Step-4: Factors of 75600

List of positive integer factors of 75600 that divides 75585 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 35, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 108, 112, 120, 126, 135, 140, 144, 150, 168, 175, 180, 189, 200, 210, 216, 225, 240, 252, 270, 280, 300, 315, 336, 350, 360, 378, 400, 420, 432, 450, 504, 525, 540, 560, 600, 630, 675, 700, 720, 756, 840, 900, 945, 1008, 1050, 1080, 1200, 1260, 1350, 1400, 1512, 1575, 1680, 1800, 1890, 2100, 2160, 2520, 2700, 2800, 3024, 3150, 3600, 3780, 4200, 4725, 5040, 5400, 6300, 7560, 8400, 9450, 10800, 12600, 15120, 18900, 25200, 37800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75585 and 75600. The biggest common factor number is the GCF number.
So the greatest common factor 75585 and 75600 is 15.

Also check out the Least Common Multiple of 75585 and 75600