Give the prime factorization of each of the following numbers :
`18`

Options

A. `2 xx 3^(4)`
B. `2 xx 3^(3)`
C. `2 xx 3^(2)`
D. `3xx 3^(2)`

Answer

To find the prime factorization of the number 18, we will follow these steps:

### Step 1: Start with the number 18.
We begin with the number we want to factor, which is 18.

### Step 2: Divide by the smallest prime number.
The smallest prime number is 2. We check if 18 is divisible by 2.
- 18 ÷ 2 = 9

### Step 3: Factor the result (9).
Now we take the quotient, which is 9, and check for prime factors.
- 9 is not divisible by 2 (since it's odd), so we try the next smallest prime number, which is 3.
- 9 ÷ 3 = 3

### Step 4: Factor the next result (3).
Now we take the quotient, which is 3.
- 3 is a prime number, so we stop here.

### Step 5: Write down the prime factors.
Now we can write down the prime factors we found:
- From our divisions, we have: 2 (from the first division) and two 3s (from the second and third divisions).
- Therefore, the prime factorization of 18 is:
\[ 18 = 2 \times 3 \times 3 \]
or we can also write it as:
\[ 18 = 2 \times 3^2 \]

### Final Answer:
The prime factorization of 18 is \( 2 \times 3^2 \).

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