What is the Greatest Common Factor of 75600 and 75608?

Greatest common factor (GCF) of 75600 and 75608 is 8.

GCF(75600,75608) = 8

We will now calculate the prime factors of 75600 and 75608, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75600 and 75608.

How to find the GCF of 75600 and 75608?

We will first find the prime factorization of 75600 and 75608. After we will calculate the factors of 75600 and 75608 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75608

Prime factors of 75608 are 2, 13, 727. Prime factorization of 75608 in exponential form is:

75608 = 2³ × 13¹ × 727¹

Step-3: Factors of 75600

List of positive integer factors of 75600 that divides 75600 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

Step-4: Factors of 75608

List of positive integer factors of 75608 that divides 75600 without a remainder.

1, 2, 4, 8, 13, 26, 52, 104, 727, 1454, 2908, 5816, 9451, 18902, 37804

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75600 and 75608. The biggest common factor number is the GCF number.
So the greatest common factor 75600 and 75608 is 8.

Also check out the Least Common Multiple of 75600 and 75608