What is the Greatest Common Factor of 17385 and 17404?

Greatest common factor (GCF) of 17385 and 17404 is 19.

GCF(17385,17404) = 19

We will now calculate the prime factors of 17385 and 17404, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17385 and 17404.

How to find the GCF of 17385 and 17404?

We will first find the prime factorization of 17385 and 17404. After we will calculate the factors of 17385 and 17404 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 17404

Prime factors of 17404 are 2, 19, 229. Prime factorization of 17404 in exponential form is:

17404 = 2² × 19¹ × 229¹

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 17404

List of positive integer factors of 17404 that divides 17385 without a remainder.

1, 2, 4, 19, 38, 76, 229, 458, 916, 4351, 8702

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17385 and 17404. The biggest common factor number is the GCF number.
So the greatest common factor 17385 and 17404 is 19.

Also check out the Least Common Multiple of 17385 and 17404