What is the Greatest Common Factor of 14688 and 14705?

Greatest common factor (GCF) of 14688 and 14705 is 17.

GCF(14688,14705) = 17

We will now calculate the prime factors of 14688 and 14705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14688 and 14705.

How to find the GCF of 14688 and 14705?

We will first find the prime factorization of 14688 and 14705. After we will calculate the factors of 14688 and 14705 and find the biggest common factor number .

Step-1: Prime Factorization of 14688

Prime factors of 14688 are 2, 3, 17. Prime factorization of 14688 in exponential form is:

14688 = 2⁵ × 3³ × 17¹

Step-2: Prime Factorization of 14705

Prime factors of 14705 are 5, 17, 173. Prime factorization of 14705 in exponential form is:

14705 = 5¹ × 17¹ × 173¹

Step-3: Factors of 14688

List of positive integer factors of 14688 that divides 14688 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 68, 72, 96, 102, 108, 136, 144, 153, 204, 216, 272, 288, 306, 408, 432, 459, 544, 612, 816, 864, 918, 1224, 1632, 1836, 2448, 3672, 4896, 7344

Step-4: Factors of 14705

List of positive integer factors of 14705 that divides 14688 without a remainder.

1, 5, 17, 85, 173, 865, 2941

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14688 and 14705. The biggest common factor number is the GCF number.
So the greatest common factor 14688 and 14705 is 17.

Also check out the Least Common Multiple of 14688 and 14705