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To determine the correct prime factorization of 6600, let's break down the number step-by-step:

### 1. Start by factoring 6600:
\[
6600 = 66 \times 100
\]
### 2. Factor 66:
\[
66 = 2 \times 3 \times 11
\]
### 3. Factor 100:
\[
100 = 2^2 \times 5^2
\]

### 4. Combine all the factors:
\[
6600 = 2^3 \times 3 \times 5^2 \times 11
\]

Now, let's compare this with the options provided:

- **Option 1:** \( 2^2 \times 3^2 \times 5^2 \times 7^2 \) — This is incorrect as it includes factors of 7 and the powers of 2 and 3 are wrong.
  
- **Option 2:** \( 2^3 \times 3 \times 5^2 \times 11 \) — This matches the correct factorization.

- **Option 3:** \( 2^2 \times 3 \times 5^2 \times 13 \) — This is incorrect because it includes a factor of 13 instead of 11 and the power of 2 is wrong.

- **Option 4:** \( 60 \times 110 \) — This is not a prime factorization, so it's incorrect.

### Correct Answer:
The correct prime factorization is **Option 2: \( 2^3 \times 3 \times 5^2 \times 11 \)**.

Do you need any further details or have questions about this process?

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Here are 5 questions related to this topic:
1. What are the steps to factor a number into its prime factors?
2. How do you handle large numbers when finding prime factorizations?
3. Why is it important to include all prime factors in the factorization?
4. Can prime factorization be applied to other areas of math?
5. What is the difference between prime factorization and regular factoring?

**Tip:** Always start with dividing the number by the smallest prime (like 2), and continue factoring until you're left with all prime numbers.

Select the prime factorization of the number 6600.

Learn how to find the prime factorization of 6600. This math problem breaks down 6600 into its prime factors: 2^3 × 3 × 5^2 × 11. Perfect for middle school students learning about prime numbers, exponents, and the Fundamental Theorem of Arithmetic.

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