What is the Greatest Common Factor of 28185 and 28200?

Greatest common factor (GCF) of 28185 and 28200 is 15.

GCF(28185,28200) = 15

We will now calculate the prime factors of 28185 and 28200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28185 and 28200.

How to find the GCF of 28185 and 28200?

We will first find the prime factorization of 28185 and 28200. After we will calculate the factors of 28185 and 28200 and find the biggest common factor number .

Step-1: Prime Factorization of 28185

Prime factors of 28185 are 3, 5, 1879. Prime factorization of 28185 in exponential form is:

28185 = 3¹ × 5¹ × 1879¹

Step-2: Prime Factorization of 28200

Prime factors of 28200 are 2, 3, 5, 47. Prime factorization of 28200 in exponential form is:

28200 = 2³ × 3¹ × 5² × 47¹

Step-3: Factors of 28185

List of positive integer factors of 28185 that divides 28185 without a remainder.

1, 3, 5, 15, 1879, 5637, 9395

Step-4: Factors of 28200

List of positive integer factors of 28200 that divides 28185 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 47, 50, 60, 75, 94, 100, 120, 141, 150, 188, 200, 235, 282, 300, 376, 470, 564, 600, 705, 940, 1128, 1175, 1410, 1880, 2350, 2820, 3525, 4700, 5640, 7050, 9400, 14100

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28185 and 28200. The biggest common factor number is the GCF number.
So the greatest common factor 28185 and 28200 is 15.

Also check out the Least Common Multiple of 28185 and 28200