Give the prime factorization of each of the following numbers :
`12 `

Options

A. `2^(2) xx 5`
B. `2^(2) xx 3`
C. `2^(2) xx 7`
D. `2^(3) xx 2`

Answer

To find the prime factorization of the number 12, we will break it down into its prime factors step by step.

### Step-by-Step Solution:

1. **Start with the number 12.**
- We want to factor 12 into prime numbers.

2. **Identify the smallest prime number.**
- The smallest prime number is 2.

3. **Check if 12 is divisible by 2.**
- Yes, 12 is divisible by 2.
- When we divide 12 by 2, we get:
\[ 12 \div 2 = 6 \]

4. **Now, take the quotient (6) and check if it is divisible by 2 again.**
- Yes, 6 is also divisible by 2.
- Dividing 6 by 2 gives:
\[ 6 \div 2 = 3 \]

5. **Now, take the quotient (3) and check if it is a prime number.**
- The number 3 is a prime number.

6. **We can now express 12 as a product of its prime factors.**
- From the divisions we performed, we have:
\[ 12 = 2 \times 2 \times 3 \]
- This can also be written as:
\[ 12 = 2^2 \times 3^1 \]

### Final Answer:
The prime factorization of 12 is:
\[ 12 = 2^2 \times 3 \]