What is the Greatest Common Factor of 82185 and 82200?

Greatest common factor (GCF) of 82185 and 82200 is 15.

GCF(82185,82200) = 15

We will now calculate the prime factors of 82185 and 82200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82185 and 82200.

How to find the GCF of 82185 and 82200?

We will first find the prime factorization of 82185 and 82200. After we will calculate the factors of 82185 and 82200 and find the biggest common factor number .

Step-1: Prime Factorization of 82185

Prime factors of 82185 are 3, 5, 5479. Prime factorization of 82185 in exponential form is:

82185 = 3¹ × 5¹ × 5479¹

Step-2: Prime Factorization of 82200

Prime factors of 82200 are 2, 3, 5, 137. Prime factorization of 82200 in exponential form is:

82200 = 2³ × 3¹ × 5² × 137¹

Step-3: Factors of 82185

List of positive integer factors of 82185 that divides 82185 without a remainder.

1, 3, 5, 15, 5479, 16437, 27395

Step-4: Factors of 82200

List of positive integer factors of 82200 that divides 82185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 137, 150, 200, 274, 300, 411, 548, 600, 685, 822, 1096, 1370, 1644, 2055, 2740, 3288, 3425, 4110, 5480, 6850, 8220, 10275, 13700, 16440, 20550, 27400, 41100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82185 and 82200. The biggest common factor number is the GCF number.
So the greatest common factor 82185 and 82200 is 15.

Also check out the Least Common Multiple of 82185 and 82200