What is the Greatest Common Factor of 75596 and 75600?

Greatest common factor (GCF) of 75596 and 75600 is 4.

GCF(75596,75600) = 4

We will now calculate the prime factors of 75596 and 75600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75596 and 75600.

How to find the GCF of 75596 and 75600?

We will first find the prime factorization of 75596 and 75600. After we will calculate the factors of 75596 and 75600 and find the biggest common factor number .

Step-1: Prime Factorization of 75596

Prime factors of 75596 are 2, 18899. Prime factorization of 75596 in exponential form is:

75596 = 2² × 18899¹

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 75596

List of positive integer factors of 75596 that divides 75596 without a remainder.

1, 2, 4, 18899, 37798

Step-4: Factors of 75600

List of positive integer factors of 75600 that divides 75596 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 75596 and 75600. The biggest common factor number is the GCF number.
So the greatest common factor 75596 and 75600 is 4.

Also check out the Least Common Multiple of 75596 and 75600