What will be the prime factors of the following?
`(i)` 32

Options

A. `2 xx 2 xx 2 xx 2 xx 2`
B. `3 xx 3 xx 2 xx2`
C. `2 xx 2 xx 8`
D. `2 xx 2 xx 2 xx 4`

Answer

To find the prime factors of 32, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number to factor**: We are given the number 32.

2. **Start dividing by the smallest prime number**: The smallest prime number is 2. We will divide 32 by 2.
- \( 32 \div 2 = 16 \)

3. **Continue dividing by 2**: We take the result (16) and divide it by 2 again.
- \( 16 \div 2 = 8 \)

4. **Repeat the division**: We continue this process.
- \( 8 \div 2 = 4 \)
- \( 4 \div 2 = 2 \)
- \( 2 \div 2 = 1 \)

5. **List the prime factors**: Each time we divided by 2, we found a prime factor. We divided by 2 a total of 5 times.
- Therefore, the prime factorization of 32 is \( 2 \times 2 \times 2 \times 2 \times 2 \) or \( 2^5 \).

### Final Answer:
The prime factors of 32 are \( 2^5 \).