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Let's work on solving the prime factorizations at the bottom of the page:

### 49. \( 2^2 \cdot 3^2 \cdot 5 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 4 \cdot 9 = 36 \)
- \( 36 \cdot 5 = 180 \)

The number represented is **180**.

### 50. \( 3^2 \cdot 5^2 \cdot 7 \)
- \( 3^2 = 9 \)
- \( 5^2 = 25 \)
- \( 9 \cdot 25 = 225 \)
- \( 225 \cdot 7 = 1575 \)

The number represented is **1575**.

### 51. \( 2^3 \cdot 11^2 \cdot 13 \)
- \( 2^3 = 8 \)
- \( 11^2 = 121 \)
- \( 8 \cdot 121 = 968 \)
- \( 968 \cdot 13 = 12584 \)

The number represented is **12584**.

Would you like any more details or clarifications on these calculations?

Here are five related questions to deepen understanding:
1. What is the prime factorization of 500?
2. How do you find the prime factorization of a number?
3. What is the greatest common divisor (GCD) of 180 and 1575?
4. Can two different numbers have the same prime factorization?
5. How can prime factorization help in simplifying fractions?

**Tip:** Prime factorizations are useful for finding the greatest common divisor (GCD) and least common multiple (LCM) between numbers.

Find the numbers represented by the following prime factorizations: 49. 2^2 * 3^2 * 5, 50. 3^2 * 5^2 * 7, 51. 2^3 * 11^2 * 13

Explore how to find the numbers represented by the prime factorizations: 2^2 * 3^2 * 5 = 180, 3^2 * 5^2 * 7 = 1575, and 2^3 * 11^2 * 13 = 12584. This tutorial covers essential prime factorization methods and is suitable for students in Grades 5-7.

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