What is the Greatest Common Factor of 13719 and 13728?

Greatest common factor (GCF) of 13719 and 13728 is 3.

GCF(13719,13728) = 3

We will now calculate the prime factors of 13719 and 13728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13719 and 13728.

How to find the GCF of 13719 and 13728?

We will first find the prime factorization of 13719 and 13728. After we will calculate the factors of 13719 and 13728 and find the biggest common factor number .

Step-1: Prime Factorization of 13719

Prime factors of 13719 are 3, 17, 269. Prime factorization of 13719 in exponential form is:

13719 = 3¹ × 17¹ × 269¹

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 13719

List of positive integer factors of 13719 that divides 13719 without a remainder.

1, 3, 17, 51, 269, 807, 4573

Step-4: Factors of 13728

List of positive integer factors of 13728 that divides 13719 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 13719 and 13728. The biggest common factor number is the GCF number.
So the greatest common factor 13719 and 13728 is 3.

Also check out the Least Common Multiple of 13719 and 13728