What is the Greatest Common Factor of 14688 and 14708?

Greatest common factor (GCF) of 14688 and 14708 is 4.

GCF(14688,14708) = 4

We will now calculate the prime factors of 14688 and 14708, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14688 and 14708.

How to find the GCF of 14688 and 14708?

We will first find the prime factorization of 14688 and 14708. After we will calculate the factors of 14688 and 14708 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 14708

Prime factors of 14708 are 2, 3677. Prime factorization of 14708 in exponential form is:

14708 = 2² × 3677¹

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 14708

List of positive integer factors of 14708 that divides 14688 without a remainder.

1, 2, 4, 3677, 7354

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14688 and 14708. The biggest common factor number is the GCF number.
So the greatest common factor 14688 and 14708 is 4.

Also check out the Least Common Multiple of 14688 and 14708