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To find the greatest common factor (GCF) of \( 10x^2 \) and \( 15x \), let's break it down step by step:

### Step 1: Prime Factorization
- \( 10x^2 = 2 \times 5 \times x \times x \)
- \( 15x = 3 \times 5 \times x \)

### Step 2: Identify the Common Factors
The common factors between \( 10x^2 \) and \( 15x \) are:
- \( 5 \) (from the constants),
- \( x \) (from the variables).

### Step 3: Combine the Common Factors
The GCF is \( 5x \).

Thus, the correct answer is:
**C. 5x**

Would you like more details on any step, or do you have any questions?

Here are five related questions to expand on this topic:
1. What is the GCF of \( 20x^2y \) and \( 25xy^2 \)?
2. How do you find the GCF of three or more terms?
3. What is the difference between the GCF and the Least Common Multiple (LCM)?
4. How do you find the GCF of numbers that include both variables and coefficients?
5. What is the GCF of \( 12x^3 \) and \( 18x^2 \)?

**Tip:** Always break down both coefficients and variables separately to find the GCF when variables are involved.

Learn how to find the greatest common factor (GCF) of 10x^2 and 15x with step-by-step instructions. This algebra problem involves factoring and prime factorization, suitable for students in Grades 7-9.

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