What is the Greatest Common Factor of 59385 and 59400?

Greatest common factor (GCF) of 59385 and 59400 is 15.

GCF(59385,59400) = 15

We will now calculate the prime factors of 59385 and 59400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59385 and 59400.

How to find the GCF of 59385 and 59400?

We will first find the prime factorization of 59385 and 59400. After we will calculate the factors of 59385 and 59400 and find the biggest common factor number .

Step-1: Prime Factorization of 59385

Prime factors of 59385 are 3, 5, 37, 107. Prime factorization of 59385 in exponential form is:

59385 = 3¹ × 5¹ × 37¹ × 107¹

Step-2: Prime Factorization of 59400

Prime factors of 59400 are 2, 3, 5, 11. Prime factorization of 59400 in exponential form is:

59400 = 2³ × 3³ × 5² × 11¹

Step-3: Factors of 59385

List of positive integer factors of 59385 that divides 59385 without a remainder.

1, 3, 5, 15, 37, 107, 111, 185, 321, 535, 555, 1605, 3959, 11877, 19795

Step-4: Factors of 59400

List of positive integer factors of 59400 that divides 59385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 25, 27, 30, 33, 36, 40, 44, 45, 50, 54, 55, 60, 66, 72, 75, 88, 90, 99, 100, 108, 110, 120, 132, 135, 150, 165, 180, 198, 200, 216, 220, 225, 264, 270, 275, 297, 300, 330, 360, 396, 440, 450, 495, 540, 550, 594, 600, 660, 675, 792, 825, 900, 990, 1080, 1100, 1188, 1320, 1350, 1485, 1650, 1800, 1980, 2200, 2376, 2475, 2700, 2970, 3300, 3960, 4950, 5400, 5940, 6600, 7425, 9900, 11880, 14850, 19800, 29700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59385 and 59400. The biggest common factor number is the GCF number.
So the greatest common factor 59385 and 59400 is 15.

Also check out the Least Common Multiple of 59385 and 59400