What is the Greatest Common Factor of 34185 and 34200?

Greatest common factor (GCF) of 34185 and 34200 is 15.

GCF(34185,34200) = 15

We will now calculate the prime factors of 34185 and 34200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34185 and 34200.

How to find the GCF of 34185 and 34200?

We will first find the prime factorization of 34185 and 34200. After we will calculate the factors of 34185 and 34200 and find the biggest common factor number .

Step-1: Prime Factorization of 34185

Prime factors of 34185 are 3, 5, 43, 53. Prime factorization of 34185 in exponential form is:

34185 = 3¹ × 5¹ × 43¹ × 53¹

Step-2: Prime Factorization of 34200

Prime factors of 34200 are 2, 3, 5, 19. Prime factorization of 34200 in exponential form is:

34200 = 2³ × 3² × 5² × 19¹

Step-3: Factors of 34185

List of positive integer factors of 34185 that divides 34185 without a remainder.

1, 3, 5, 15, 43, 53, 129, 159, 215, 265, 645, 795, 2279, 6837, 11395

Step-4: Factors of 34200

List of positive integer factors of 34200 that divides 34185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 19, 20, 24, 25, 30, 36, 38, 40, 45, 50, 57, 60, 72, 75, 76, 90, 95, 100, 114, 120, 150, 152, 171, 180, 190, 200, 225, 228, 285, 300, 342, 360, 380, 450, 456, 475, 570, 600, 684, 760, 855, 900, 950, 1140, 1368, 1425, 1710, 1800, 1900, 2280, 2850, 3420, 3800, 4275, 5700, 6840, 8550, 11400, 17100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34185 and 34200. The biggest common factor number is the GCF number.
So the greatest common factor 34185 and 34200 is 15.

Also check out the Least Common Multiple of 34185 and 34200