What is the Greatest Common Factor of 13872 and 13884?

Greatest common factor (GCF) of 13872 and 13884 is 12.

GCF(13872,13884) = 12

We will now calculate the prime factors of 13872 and 13884, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13872 and 13884.

How to find the GCF of 13872 and 13884?

We will first find the prime factorization of 13872 and 13884. After we will calculate the factors of 13872 and 13884 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 13884

Prime factors of 13884 are 2, 3, 13, 89. Prime factorization of 13884 in exponential form is:

13884 = 2² × 3¹ × 13¹ × 89¹

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 13884

List of positive integer factors of 13884 that divides 13872 without a remainder.

1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 89, 156, 178, 267, 356, 534, 1068, 1157, 2314, 3471, 4628, 6942

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13872 and 13884. The biggest common factor number is the GCF number.
So the greatest common factor 13872 and 13884 is 12.

Also check out the Least Common Multiple of 13872 and 13884