To determine the prime factorization of [tex]\(18\)[/tex], we need to break it down into its prime factors step-by-step. Here's how it can be done:
1. Start with 18:
[tex]\[
18
\][/tex]
2. Find the smallest prime that divides 18:
The smallest prime number is [tex]\(2\)[/tex]. Check if [tex]\(18\)[/tex] is divisible by [tex]\(2\)[/tex]:
[tex]\[
18 \div 2 = 9
\][/tex]
So, we have:
[tex]\[
18 = 2 \times 9
\][/tex]
3. Factorize 9 further:
Now we focus on [tex]\(9\)[/tex]. The smallest prime number that divides [tex]\(9\)[/tex] is [tex]\(3\)[/tex]:
[tex]\[
9 \div 3 = 3
\][/tex]
And:
[tex]\[
3 \div 3 = 1
\][/tex]
Thus, [tex]\(9\)[/tex] can be expressed as:
[tex]\[
9 = 3 \times 3 = 3^2
\][/tex]
4. Combine all the factors:
Substitute back to express [tex]\(18\)[/tex] fully in terms of its prime factors:
[tex]\[
18 = 2 \times 9 = 2 \times 3 \times 3 = 2 \times 3^2
\][/tex]
Hence, the prime factorization of [tex]\(18\)[/tex] is:
[tex]\[
2 \times 3^2
\][/tex]
Therefore, among the given options, the correct representation of the prime factorization of [tex]\(18\)[/tex] is:
[tex]\[
2 \times 3^2
\][/tex]
