What is the Greatest Common Factor of 52185 and 52200?

Greatest common factor (GCF) of 52185 and 52200 is 15.

GCF(52185,52200) = 15

We will now calculate the prime factors of 52185 and 52200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52185 and 52200.

How to find the GCF of 52185 and 52200?

We will first find the prime factorization of 52185 and 52200. After we will calculate the factors of 52185 and 52200 and find the biggest common factor number .

Step-1: Prime Factorization of 52185

Prime factors of 52185 are 3, 5, 7, 71. Prime factorization of 52185 in exponential form is:

52185 = 3¹ × 5¹ × 7² × 71¹

Step-2: Prime Factorization of 52200

Prime factors of 52200 are 2, 3, 5, 29. Prime factorization of 52200 in exponential form is:

52200 = 2³ × 3² × 5² × 29¹

Step-3: Factors of 52185

List of positive integer factors of 52185 that divides 52185 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 71, 105, 147, 213, 245, 355, 497, 735, 1065, 1491, 2485, 3479, 7455, 10437, 17395

Step-4: Factors of 52200

List of positive integer factors of 52200 that divides 52185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 29, 30, 36, 40, 45, 50, 58, 60, 72, 75, 87, 90, 100, 116, 120, 145, 150, 174, 180, 200, 225, 232, 261, 290, 300, 348, 360, 435, 450, 522, 580, 600, 696, 725, 870, 900, 1044, 1160, 1305, 1450, 1740, 1800, 2088, 2175, 2610, 2900, 3480, 4350, 5220, 5800, 6525, 8700, 10440, 13050, 17400, 26100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52185 and 52200. The biggest common factor number is the GCF number.
So the greatest common factor 52185 and 52200 is 15.

Also check out the Least Common Multiple of 52185 and 52200