What is the Greatest Common Factor of 14400 and 14407?

Greatest common factor (GCF) of 14400 and 14407 is 1.

GCF(14400,14407) = 1

We will now calculate the prime factors of 14400 and 14407, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14400 and 14407.

How to find the GCF of 14400 and 14407?

We will first find the prime factorization of 14400 and 14407. After we will calculate the factors of 14400 and 14407 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 14407

Prime factors of 14407 are 14407. Prime factorization of 14407 in exponential form is:

14407 = 14407¹

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 14407

List of positive integer factors of 14407 that divides 14400 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14400 and 14407. The biggest common factor number is the GCF number.
So the greatest common factor 14400 and 14407 is 1.

Also check out the Least Common Multiple of 14400 and 14407