To find the greatest common factor (GCF) of 54 and 72 using their prime factorizations, we first list out the prime factorizations:
- 54: \(2^1 \times 3^3\)
- 72: \(2^3 \times 3^2\)
Next, we identify the lowest power of each common prime factor:
- For 2, the lowest power is \(2^1\) (from 54).
- For 3, the lowest power is \(3^2\) (from 72).
Now, we multiply these common prime factors together:
\[ \text{GCF} = 2^1 \times 3^2 = 2 \times 9 = 18 \]
So, looking at the provided options:
- \(2 \times 3\) = 6
- \(2 \times 3 \times 3\) = 18 (this is the correct answer!)
- \(2 \times 2 \times 3 \times 3\) = 36
- \(2 \times 2 \times 2 \times 3 \times 3 \times 3\) = 108
Thus, the greatest common factor of 54 and 72 is \(2 \times 3 \times 3\) or \(18\).