What is the Greatest Common Factor of 17400 and 17404?

Greatest common factor (GCF) of 17400 and 17404 is 4.

GCF(17400,17404) = 4

We will now calculate the prime factors of 17400 and 17404, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17400 and 17404.

How to find the GCF of 17400 and 17404?

We will first find the prime factorization of 17400 and 17404. After we will calculate the factors of 17400 and 17404 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 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 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 17404

List of positive integer factors of 17404 that divides 17400 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 17400 and 17404. The biggest common factor number is the GCF number.
So the greatest common factor 17400 and 17404 is 4.

Also check out the Least Common Multiple of 17400 and 17404