What is the Greatest Common Factor of 13872 and 13887?

Greatest common factor (GCF) of 13872 and 13887 is 3.

GCF(13872,13887) = 3

We will now calculate the prime factors of 13872 and 13887, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13872 and 13887.

How to find the GCF of 13872 and 13887?

We will first find the prime factorization of 13872 and 13887. After we will calculate the factors of 13872 and 13887 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13887

Prime factors of 13887 are 3, 1543. Prime factorization of 13887 in exponential form is:

13887 = 3² × 1543¹

Step-3: Factors of 13872

List of positive integer factors of 13872 that divides 13872 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

Step-4: Factors of 13887

List of positive integer factors of 13887 that divides 13872 without a remainder.

1, 3, 9, 1543, 4629

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13872 and 13887. The biggest common factor number is the GCF number.
So the greatest common factor 13872 and 13887 is 3.

Also check out the Least Common Multiple of 13872 and 13887