What is the Greatest Common Factor of 14400 and 14415?

Greatest common factor (GCF) of 14400 and 14415 is 15.

GCF(14400,14415) = 15

We will now calculate the prime factors of 14400 and 14415, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14400 and 14415.

How to find the GCF of 14400 and 14415?

We will first find the prime factorization of 14400 and 14415. After we will calculate the factors of 14400 and 14415 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 14415

Prime factors of 14415 are 3, 5, 31. Prime factorization of 14415 in exponential form is:

14415 = 3¹ × 5¹ × 31²

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 14415

List of positive integer factors of 14415 that divides 14400 without a remainder.

1, 3, 5, 15, 31, 93, 155, 465, 961, 2883, 4805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14400 and 14415. The biggest common factor number is the GCF number.
So the greatest common factor 14400 and 14415 is 15.

Also check out the Least Common Multiple of 14400 and 14415