What is the Greatest Common Factor of 14400 and 14404?

Greatest common factor (GCF) of 14400 and 14404 is 4.

GCF(14400,14404) = 4

We will now calculate the prime factors of 14400 and 14404, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14400 and 14404.

How to find the GCF of 14400 and 14404?

We will first find the prime factorization of 14400 and 14404. After we will calculate the factors of 14400 and 14404 and find the biggest common factor number .

Step-1: Prime Factorization of 14400

Prime factors of 14400 are 2, 3, 5. Prime factorization of 14400 in exponential form is:

14400 = 2⁶ × 3² × 5²

Step-2: Prime Factorization of 14404

Prime factors of 14404 are 2, 13, 277. Prime factorization of 14404 in exponential form is:

14404 = 2² × 13¹ × 277¹

Step-3: Factors of 14400

List of positive integer factors of 14400 that divides 14400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 400, 450, 480, 576, 600, 720, 800, 900, 960, 1200, 1440, 1600, 1800, 2400, 2880, 3600, 4800, 7200

Step-4: Factors of 14404

List of positive integer factors of 14404 that divides 14400 without a remainder.

1, 2, 4, 13, 26, 52, 277, 554, 1108, 3601, 7202

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14400 and 14404. The biggest common factor number is the GCF number.
So the greatest common factor 14400 and 14404 is 4.

Also check out the Least Common Multiple of 14400 and 14404