To determine the prime factorization of 28, we need to break it down into its prime factors—numbers that are only divisible by 1 and themselves.
1. Identify the smallest prime number that divides 28:
Since 28 is even, it is divisible by 2. Dividing 28 by 2, we get:
[tex]\[
28 \div 2 = 14
\][/tex]
So, 2 is a prime factor, and we have now:
[tex]\[
28 = 2 \times 14
\][/tex]
2. Repeat the process with the resulting quotient (14):
14 is also even, so it is again divisible by 2. Dividing 14 by 2, we get:
[tex]\[
14 \div 2 = 7
\][/tex]
So, another 2 is a prime factor, and we have now:
[tex]\[
28 = 2 \times 2 \times 7
\][/tex]
3. Examine the remaining number (7):
7 is a prime number because it is only divisible by 1 and 7. Therefore, we can include it as a prime factor.
So, the prime factorization of 28 is:
[tex]\[
28 = 2 \times 2 \times 7
\][/tex]
Looking at the provided options:
- A. [tex]\(28 = 2 \times 2 \times 7\)[/tex]
- B. [tex]\(28 = 2 \times 2 \times 3 \times 3\)[/tex]
- C. [tex]\(28 = 2 \times 14\)[/tex]
- D. [tex]\(28 = 4 \times 7\)[/tex]
Option A is the correct representation of the prime factorization of 28. Therefore, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
