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The problem involves completing the prime factorization of 280. We are given part of the prime factorization as \( 2^3 \cdot 5 \), and we need to determine the missing factor.

### Step-by-step solution:
1. **Prime factorization of 280**:  
   First, let's find the complete prime factorization of 280:
   \[
   280 \div 2 = 140
   \]
   \[
   140 \div 2 = 70
   \]
   \[
   70 \div 2 = 35
   \]
   Now, 35 is not divisible by 2, so we move to the next prime number, 5:
   \[
   35 \div 5 = 7
   \]
   Now we have 7, which is a prime number.

   So, the prime factorization of 280 is:
   \[
   2^3 \cdot 5 \cdot 7
   \]

2. **Identifying the missing factor**:  
   The given factorization is \( 2^3 \cdot 5 \), and comparing it with the full factorization \( 2^3 \cdot 5 \cdot 7 \), the missing factor is **7**.

Thus, the correct answer is:
\[
\boxed{d. \ 7}
\]

Would you like a detailed explanation or have any further questions?

### Related Questions:
1. What are the steps to perform prime factorization for any number?
2. Can you explain how exponents work in prime factorizations?
3. How do we know when to stop the prime factorization process?
4. Why are prime numbers important in mathematics?
5. How do prime factorizations help in simplifying fractions?

### Tip:
Always start dividing by the smallest prime numbers (2, 3, 5, etc.) when performing prime factorization to ensure accuracy.

Mrs. Roman showed students part of the prime factorization of 280. One factor is missing. 2^3 * 5 * ? Which number completes this prime factorization?

Learn how to complete the prime factorization of 280. This problem asks to find the missing factor in the given partial factorization 2^3 * 5. The full prime factorization is 2^3 * 5 * 7, with 7 being the missing number. Suitable for students in Grades 5-7.

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