What is the Greatest Common Factor of 89385 and 89400?

Greatest common factor (GCF) of 89385 and 89400 is 15.

GCF(89385,89400) = 15

We will now calculate the prime factors of 89385 and 89400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89385 and 89400.

How to find the GCF of 89385 and 89400?

We will first find the prime factorization of 89385 and 89400. After we will calculate the factors of 89385 and 89400 and find the biggest common factor number .

Step-1: Prime Factorization of 89385

Prime factors of 89385 are 3, 5, 59, 101. Prime factorization of 89385 in exponential form is:

89385 = 3¹ × 5¹ × 59¹ × 101¹

Step-2: Prime Factorization of 89400

Prime factors of 89400 are 2, 3, 5, 149. Prime factorization of 89400 in exponential form is:

89400 = 2³ × 3¹ × 5² × 149¹

Step-3: Factors of 89385

List of positive integer factors of 89385 that divides 89385 without a remainder.

1, 3, 5, 15, 59, 101, 177, 295, 303, 505, 885, 1515, 5959, 17877, 29795

Step-4: Factors of 89400

List of positive integer factors of 89400 that divides 89385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 149, 150, 200, 298, 300, 447, 596, 600, 745, 894, 1192, 1490, 1788, 2235, 2980, 3576, 3725, 4470, 5960, 7450, 8940, 11175, 14900, 17880, 22350, 29800, 44700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89385 and 89400. The biggest common factor number is the GCF number.
So the greatest common factor 89385 and 89400 is 15.

Also check out the Least Common Multiple of 89385 and 89400