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To find the greatest common factor (GCF) of \(16d\) and \(24d\), let's break down the problem:

1. **Factor Out \(d\):** Since \(d\) is a common factor of both \(16d\) and \(24d\), the GCF must include \(d\).
2. **Find GCF of 16 and 24:** Next, we find the GCF of the coefficients, 16 and 24.

   - The prime factors of 16 are: \(2^4\).
   - The prime factors of 24 are: \(2^3 \times 3\).
   - The highest common factor of 16 and 24 is \(2^3 = 8\).

3. **Combine Results:** Therefore, the GCF of \(16d\) and \(24d\) is \(8d\).

### Answer
The GCF of \(16d\) and \(24d\) is \(8d\).

Would you like a detailed explanation on finding GCFs? Let me know if you have any questions!

### Related Questions
1. What is the GCF of \(12d\) and \(18d\)?
2. How do you calculate the GCF of two numbers with different variables, like \(16d\) and \(24d^2\)?
3. Can the GCF be greater than one of the original numbers?
4. How does the presence of a variable affect finding the GCF?
5. What are some real-world applications of finding the GCF?

### Tip
When factoring out the GCF from terms with variables, separate the coefficients from the variables first to simplify the process.

If d is a positive integer, which value below represents the GCF of 16d and 24d?

Learn how to find the greatest common factor (GCF) of 16d and 24d, breaking down the steps of factoring out variables and using prime factorization. This guide simplifies the GCF process for expressions with variables, ideal for middle school math students.

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