What is the Greatest Common Factor of 14400 and 14417?

Greatest common factor (GCF) of 14400 and 14417 is 1.

GCF(14400,14417) = 1

We will now calculate the prime factors of 14400 and 14417, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14400 and 14417.

How to find the GCF of 14400 and 14417?

We will first find the prime factorization of 14400 and 14417. After we will calculate the factors of 14400 and 14417 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 14417

Prime factors of 14417 are 13, 1109. Prime factorization of 14417 in exponential form is:

14417 = 13¹ × 1109¹

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 14417

List of positive integer factors of 14417 that divides 14400 without a remainder.

1, 13, 1109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14400 and 14417. The biggest common factor number is the GCF number.
So the greatest common factor 14400 and 14417 is 1.

Also check out the Least Common Multiple of 14400 and 14417