What is the Greatest Common Factor of 13728 and 13746?

Greatest common factor (GCF) of 13728 and 13746 is 6.

GCF(13728,13746) = 6

We will now calculate the prime factors of 13728 and 13746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13728 and 13746.

How to find the GCF of 13728 and 13746?

We will first find the prime factorization of 13728 and 13746. After we will calculate the factors of 13728 and 13746 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13746

Prime factors of 13746 are 2, 3, 29, 79. Prime factorization of 13746 in exponential form is:

13746 = 2¹ × 3¹ × 29¹ × 79¹

Step-3: Factors of 13728

List of positive integer factors of 13728 that divides 13728 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

Step-4: Factors of 13746

List of positive integer factors of 13746 that divides 13728 without a remainder.

1, 2, 3, 6, 29, 58, 79, 87, 158, 174, 237, 474, 2291, 4582, 6873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13728 and 13746. The biggest common factor number is the GCF number.
So the greatest common factor 13728 and 13746 is 6.

Also check out the Least Common Multiple of 13728 and 13746