What is the Greatest Common Factor of 75590 and 75600?

Greatest common factor (GCF) of 75590 and 75600 is 10.

GCF(75590,75600) = 10

We will now calculate the prime factors of 75590 and 75600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75590 and 75600.

How to find the GCF of 75590 and 75600?

We will first find the prime factorization of 75590 and 75600. After we will calculate the factors of 75590 and 75600 and find the biggest common factor number .

Step-1: Prime Factorization of 75590

Prime factors of 75590 are 2, 5, 7559. Prime factorization of 75590 in exponential form is:

75590 = 2¹ × 5¹ × 7559¹

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 75590

List of positive integer factors of 75590 that divides 75590 without a remainder.

1, 2, 5, 10, 7559, 15118, 37795

Step-4: Factors of 75600

List of positive integer factors of 75600 that divides 75590 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 75590 and 75600. The biggest common factor number is the GCF number.
So the greatest common factor 75590 and 75600 is 10.

Also check out the Least Common Multiple of 75590 and 75600