Which of the following is the greatest common factor of 12 and 16?

To find the greatest common factor (GCF) of 12 and 16, we first determine the prime factorizations of both numbers. The prime factorization of 12 is (2^2 \times 3), and for 16, it is (2^4).

Next, we identify the common prime factors between the two numbers. Both numbers share the prime factor 2. To find the GCF, we take the lowest power of the common prime factor(s). In this case, the lowest power of 2 common to both factorizations is (2^2), which equals 4.

Thus, the greatest common factor of 12 and 16 is 4, making it the correct answer.

This option is correct because it's derived from the factorization method, accurately reflecting the greatest number that divides both 12 and 16 without remaining. Lower numbers, such as 2 or 3, do divide both but do not represent the highest factor that they share. Similarly, 6 does not divide 12 evenly, confirming that 4 is indeed the highest.