What is the Greatest Common Factor of 36585 and 36600?

Greatest common factor (GCF) of 36585 and 36600 is 15.

GCF(36585,36600) = 15

We will now calculate the prime factors of 36585 and 36600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36585 and 36600.

How to find the GCF of 36585 and 36600?

We will first find the prime factorization of 36585 and 36600. After we will calculate the factors of 36585 and 36600 and find the biggest common factor number .

Step-1: Prime Factorization of 36585

Prime factors of 36585 are 3, 5, 271. Prime factorization of 36585 in exponential form is:

36585 = 3³ × 5¹ × 271¹

Step-2: Prime Factorization of 36600

Prime factors of 36600 are 2, 3, 5, 61. Prime factorization of 36600 in exponential form is:

36600 = 2³ × 3¹ × 5² × 61¹

Step-3: Factors of 36585

List of positive integer factors of 36585 that divides 36585 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 271, 813, 1355, 2439, 4065, 7317, 12195

Step-4: Factors of 36600

List of positive integer factors of 36600 that divides 36585 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 61, 75, 100, 120, 122, 150, 183, 200, 244, 300, 305, 366, 488, 600, 610, 732, 915, 1220, 1464, 1525, 1830, 2440, 3050, 3660, 4575, 6100, 7320, 9150, 12200, 18300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36585 and 36600. The biggest common factor number is the GCF number.
So the greatest common factor 36585 and 36600 is 15.

Also check out the Least Common Multiple of 36585 and 36600