What is the Greatest Common Factor of 75600 and 75618?

Greatest common factor (GCF) of 75600 and 75618 is 18.

GCF(75600,75618) = 18

We will now calculate the prime factors of 75600 and 75618, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75600 and 75618.

How to find the GCF of 75600 and 75618?

We will first find the prime factorization of 75600 and 75618. After we will calculate the factors of 75600 and 75618 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 75618

Prime factors of 75618 are 2, 3, 4201. Prime factorization of 75618 in exponential form is:

75618 = 2¹ × 3² × 4201¹

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 75618

List of positive integer factors of 75618 that divides 75600 without a remainder.

1, 2, 3, 6, 9, 18, 4201, 8402, 12603, 25206, 37809

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75600 and 75618. The biggest common factor number is the GCF number.
So the greatest common factor 75600 and 75618 is 18.

Also check out the Least Common Multiple of 75600 and 75618