What is the Greatest Common Factor of 73185 and 73200?

Greatest common factor (GCF) of 73185 and 73200 is 15.

GCF(73185,73200) = 15

We will now calculate the prime factors of 73185 and 73200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73185 and 73200.

How to find the GCF of 73185 and 73200?

We will first find the prime factorization of 73185 and 73200. After we will calculate the factors of 73185 and 73200 and find the biggest common factor number .

Step-1: Prime Factorization of 73185

Prime factors of 73185 are 3, 5, 7, 17, 41. Prime factorization of 73185 in exponential form is:

73185 = 3¹ × 5¹ × 7¹ × 17¹ × 41¹

Step-2: Prime Factorization of 73200

Prime factors of 73200 are 2, 3, 5, 61. Prime factorization of 73200 in exponential form is:

73200 = 2⁴ × 3¹ × 5² × 61¹

Step-3: Factors of 73185

List of positive integer factors of 73185 that divides 73185 without a remainder.

1, 3, 5, 7, 15, 17, 21, 35, 41, 51, 85, 105, 119, 123, 205, 255, 287, 357, 595, 615, 697, 861, 1435, 1785, 2091, 3485, 4305, 4879, 10455, 14637, 24395

Step-4: Factors of 73200

List of positive integer factors of 73200 that divides 73185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 61, 75, 80, 100, 120, 122, 150, 183, 200, 240, 244, 300, 305, 366, 400, 488, 600, 610, 732, 915, 976, 1200, 1220, 1464, 1525, 1830, 2440, 2928, 3050, 3660, 4575, 4880, 6100, 7320, 9150, 12200, 14640, 18300, 24400, 36600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73185 and 73200. The biggest common factor number is the GCF number.
So the greatest common factor 73185 and 73200 is 15.

Also check out the Least Common Multiple of 73185 and 73200