What is the Greatest Common Factor of 13728 and 13742?

Greatest common factor (GCF) of 13728 and 13742 is 2.

GCF(13728,13742) = 2

We will now calculate the prime factors of 13728 and 13742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13728 and 13742.

How to find the GCF of 13728 and 13742?

We will first find the prime factorization of 13728 and 13742. After we will calculate the factors of 13728 and 13742 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 13742

Prime factors of 13742 are 2, 6871. Prime factorization of 13742 in exponential form is:

13742 = 2¹ × 6871¹

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 13742

List of positive integer factors of 13742 that divides 13728 without a remainder.

1, 2, 6871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13728 and 13742. The biggest common factor number is the GCF number.
So the greatest common factor 13728 and 13742 is 2.

Also check out the Least Common Multiple of 13728 and 13742