What is the Greatest Common Factor of 13856 and 13872?

Greatest common factor (GCF) of 13856 and 13872 is 16.

GCF(13856,13872) = 16

We will now calculate the prime factors of 13856 and 13872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13856 and 13872.

How to find the GCF of 13856 and 13872?

We will first find the prime factorization of 13856 and 13872. After we will calculate the factors of 13856 and 13872 and find the biggest common factor number .

Step-1: Prime Factorization of 13856

Prime factors of 13856 are 2, 433. Prime factorization of 13856 in exponential form is:

13856 = 2⁵ × 433¹

Step-2: Prime Factorization of 13872

Prime factors of 13872 are 2, 3, 17. Prime factorization of 13872 in exponential form is:

13872 = 2⁴ × 3¹ × 17²

Step-3: Factors of 13856

List of positive integer factors of 13856 that divides 13856 without a remainder.

1, 2, 4, 8, 16, 32, 433, 866, 1732, 3464, 6928

Step-4: Factors of 13872

List of positive integer factors of 13872 that divides 13856 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 289, 408, 578, 816, 867, 1156, 1734, 2312, 3468, 4624, 6936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13856 and 13872. The biggest common factor number is the GCF number.
So the greatest common factor 13856 and 13872 is 16.

Also check out the Least Common Multiple of 13856 and 13872