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To solve this problem, we need to simplify the fraction \(\frac{24x^2y^3}{32xy^5}\) by dividing both the numerator and denominator by their greatest common factor (GCF).

### Step 1: Identify the GCF
1. **Coefficients:** The GCF of 24 and 32 is 8.
2. **Variable \(x\):** The smallest power of \(x\) in both terms is \(x\).
3. **Variable \(y\):** The smallest power of \(y\) in both terms is \(y^3\).

Thus, the GCF is \(8xy^3\).

### Step 2: Simplify by Dividing by the GCF
Now, we divide both the numerator and the denominator by \(8xy^3\):

\[
\frac{24x^2y^3}{32xy^5} = \frac{24x^2y^3 \div 8xy^3}{32xy^5 \div 8xy^3} = \frac{3x}{4y^2}
\]

### Answer
The correct option is:
\[
\frac{3x}{4y^2}, \text{ Greatest Common Factor } = 8xy^3
\]

Would you like a deeper explanation, or do you have any other questions?

Here are 5 related questions to extend your understanding:
1. How do you find the GCF of two polynomials?
2. What happens to the powers of variables when dividing terms with common factors?
3. Why is it important to simplify fractions in algebra?
4. How would the answer change if we had different powers of \(x\) or \(y\) in the numerator or denominator?
5. How does factoring out the GCF help in simplifying complex algebraic expressions?

**Tip:** Always check the powers of variables when simplifying; the smallest power common to both terms is key for factoring.

Reduce the following algebraic fraction by removing the common factors and name the greatest common factor:
\(\frac{24x^2y^3}{32xy^5}\)

Learn how to simplify the algebraic fraction 24x^2y^3 / 32xy^5 by removing common factors and identifying the greatest common factor. This solution walks through key algebra concepts, including the Greatest Common Factor (GCF), with a detailed breakdown. Ideal for students in Grades 8-10.

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