What is the Greatest Common Factor of 13708 and 13728?

Greatest common factor (GCF) of 13708 and 13728 is 4.

GCF(13708,13728) = 4

We will now calculate the prime factors of 13708 and 13728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13708 and 13728.

How to find the GCF of 13708 and 13728?

We will first find the prime factorization of 13708 and 13728. After we will calculate the factors of 13708 and 13728 and find the biggest common factor number .

Step-1: Prime Factorization of 13708

Prime factors of 13708 are 2, 23, 149. Prime factorization of 13708 in exponential form is:

13708 = 2² × 23¹ × 149¹

Step-2: Prime Factorization of 13728

Prime factors of 13728 are 2, 3, 11, 13. Prime factorization of 13728 in exponential form is:

13728 = 2⁵ × 3¹ × 11¹ × 13¹

Step-3: Factors of 13708

List of positive integer factors of 13708 that divides 13708 without a remainder.

1, 2, 4, 23, 46, 92, 149, 298, 596, 3427, 6854

Step-4: Factors of 13728

List of positive integer factors of 13728 that divides 13708 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 32, 33, 39, 44, 48, 52, 66, 78, 88, 96, 104, 132, 143, 156, 176, 208, 264, 286, 312, 352, 416, 429, 528, 572, 624, 858, 1056, 1144, 1248, 1716, 2288, 3432, 4576, 6864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13708 and 13728. The biggest common factor number is the GCF number.
So the greatest common factor 13708 and 13728 is 4.

Also check out the Least Common Multiple of 13708 and 13728