What is the Greatest Common Factor of 75600 and 75610?

Greatest common factor (GCF) of 75600 and 75610 is 10.

GCF(75600,75610) = 10

We will now calculate the prime factors of 75600 and 75610, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75600 and 75610.

How to find the GCF of 75600 and 75610?

We will first find the prime factorization of 75600 and 75610. After we will calculate the factors of 75600 and 75610 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 75610

Prime factors of 75610 are 2, 5, 7561. Prime factorization of 75610 in exponential form is:

75610 = 2¹ × 5¹ × 7561¹

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 75610

List of positive integer factors of 75610 that divides 75600 without a remainder.

1, 2, 5, 10, 7561, 15122, 37805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75600 and 75610. The biggest common factor number is the GCF number.
So the greatest common factor 75600 and 75610 is 10.

Also check out the Least Common Multiple of 75600 and 75610