To find the prime factorization of [tex]\(100\)[/tex] using a factor tree, let's break down the step-by-step process:
1. Start with the number 100: The goal is to break it down into prime factors gradually.
2. Divide by the smallest prime number:
[tex]\[
100 \div 2 = 50
\][/tex]
So, [tex]\(100\)[/tex] can be expressed as [tex]\(2 \times 50\)[/tex].
3. Continue factoring 50:
[tex]\[
50 \div 2 = 25
\][/tex]
Hence, [tex]\(50\)[/tex] can be expressed as [tex]\(2 \times 25\)[/tex].
4. Factor 25 further:
[tex]\[
25 \div 5 = 5
\][/tex]
So, [tex]\(25\)[/tex] can be expressed as [tex]\(5 \times 5\)[/tex].
Now, we have broken down [tex]\(100\)[/tex] into its prime factors:
[tex]\[
100 = 2 \times 2 \times 5 \times 5
\][/tex]
Therefore, the prime factorization of [tex]\(100\)[/tex] is:
[tex]\(\boxed{2 \times 2 \times 5 \times 5}\)[/tex]
Looking at the options provided:
- [tex]\(2 \times 5\)[/tex]
- [tex]\(2 \times 2 \times 5 \times 5\)[/tex]
- [tex]\(2 \times 5 \times 10\)[/tex]
- [tex]\(10 \times 10\)[/tex]
The correct prime factorization is:
[tex]\[
\boxed{2 \times 2 \times 5 \times 5}
\][/tex]
