To find the greatest common factor (GCF) of 16 and 24 using their prime factorizations, we first identify the common prime factors and then use the lowest powers.
- The prime factorization of 16 is \(2^4\) (which means \(2\) appears four times).
- The prime factorization of 24 is \(2^3 \times 3\) (which means \(2\) appears three times and \(3\) appears once).
The common prime factor between 16 and 24 is \(2\).
- For \(2\), the lowest power in the factorizations is \(2^3\) (since \(16\) has \(2^4\) and \(24\) has \(2^3\)).
Thus, the GCF is: \[ 2^3 = 2 \times 2 \times 2 \]
Therefore, the GCF of 16 and 24 is \(2 \times 2 \times 2\), which corresponds to option C.
Answer: C. \(2 \times 2 \times 2\)
1 answer