What is the Greatest Common Factor of 14385 and 14400?

Greatest common factor (GCF) of 14385 and 14400 is 15.

GCF(14385,14400) = 15

We will now calculate the prime factors of 14385 and 14400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14385 and 14400.

How to find the GCF of 14385 and 14400?

We will first find the prime factorization of 14385 and 14400. After we will calculate the factors of 14385 and 14400 and find the biggest common factor number .

Step-1: Prime Factorization of 14385

Prime factors of 14385 are 3, 5, 7, 137. Prime factorization of 14385 in exponential form is:

14385 = 3¹ × 5¹ × 7¹ × 137¹

Step-2: 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-3: Factors of 14385

List of positive integer factors of 14385 that divides 14385 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 137, 411, 685, 959, 2055, 2877, 4795

Step-4: Factors of 14400

List of positive integer factors of 14400 that divides 14385 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14385 and 14400. The biggest common factor number is the GCF number.
So the greatest common factor 14385 and 14400 is 15.

Also check out the Least Common Multiple of 14385 and 14400