What is the Greatest Common Factor of 17400 and 17409?

Greatest common factor (GCF) of 17400 and 17409 is 3.

GCF(17400,17409) = 3

We will now calculate the prime factors of 17400 and 17409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17400 and 17409.

How to find the GCF of 17400 and 17409?

We will first find the prime factorization of 17400 and 17409. After we will calculate the factors of 17400 and 17409 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17409

Prime factors of 17409 are 3, 7, 829. Prime factorization of 17409 in exponential form is:

17409 = 3¹ × 7¹ × 829¹

Step-3: Factors of 17400

List of positive integer factors of 17400 that divides 17400 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

Step-4: Factors of 17409

List of positive integer factors of 17409 that divides 17400 without a remainder.

1, 3, 7, 21, 829, 2487, 5803

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17400 and 17409. The biggest common factor number is the GCF number.
So the greatest common factor 17400 and 17409 is 3.

Also check out the Least Common Multiple of 17400 and 17409