Question

The prime factorizations of 16 and 24 are shown below.

Prime factorization of 16: 2, 2, 2, 2
Prime factorization of 24: 2, 2, 2, 3

Using the prime factorizations, what is the greatest common factor of 16 and 24?
A.2
B.2 ´ 2
C.2 ´ 2 ´ 2
D.2 ´ 2 ´ 2 ´ 2 ´ 3

Answer 1

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. \(2 \times 2 \times 2\)**