What is the Greatest Common Factor of 17385 and 17400?

Greatest common factor (GCF) of 17385 and 17400 is 15.

GCF(17385,17400) = 15

We will now calculate the prime factors of 17385 and 17400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17385 and 17400.

How to find the GCF of 17385 and 17400?

We will first find the prime factorization of 17385 and 17400. After we will calculate the factors of 17385 and 17400 and find the biggest common factor number .

Step-1: Prime Factorization of 17385

Prime factors of 17385 are 3, 5, 19, 61. Prime factorization of 17385 in exponential form is:

17385 = 3¹ × 5¹ × 19¹ × 61¹

Step-2: Prime Factorization of 17400

Prime factors of 17400 are 2, 3, 5, 29. Prime factorization of 17400 in exponential form is:

17400 = 2³ × 3¹ × 5² × 29¹

Step-3: Factors of 17385

List of positive integer factors of 17385 that divides 17385 without a remainder.

1, 3, 5, 15, 19, 57, 61, 95, 183, 285, 305, 915, 1159, 3477, 5795

Step-4: Factors of 17400

List of positive integer factors of 17400 that divides 17385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 29, 30, 40, 50, 58, 60, 75, 87, 100, 116, 120, 145, 150, 174, 200, 232, 290, 300, 348, 435, 580, 600, 696, 725, 870, 1160, 1450, 1740, 2175, 2900, 3480, 4350, 5800, 8700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17385 and 17400. The biggest common factor number is the GCF number.
So the greatest common factor 17385 and 17400 is 15.

Also check out the Least Common Multiple of 17385 and 17400