Alicia bought some notebooks and paid Php24.00. Susan bought the same kind of notebook and paid Php16.00. What is the greatest amount each notebook can possibly cost?

To determine the greatest possible cost of each notebook, we need to find the greatest common divisor (GCD) of the amounts that Alicia and Susan paid for the notebooks. This is because the price per notebook must be a factor of both the total amounts paid by Alicia and Susan.

### Step-by-step Solution:

1. **Amounts paid:**
   - Alicia paid: Php 24.00
   - Susan paid: Php 16.00

2. **Understanding the problem:**
   - Let the cost of one notebook be \(x\) pesos.
   - The number of notebooks Alicia bought is \( \frac{24}{x} \).
   - The number of notebooks Susan bought is \( \frac{16}{x} \).
   - \(x\) must be a common divisor of both 24 and 16.

3. **Find the GCD of 24 and 16:**

   - **Prime factorization:**
     - \(24 = 2^3 \times 3^1\)
     - \(16 = 2^4\)

   - **GCD:**
     - The GCD is found by taking the lowest power of all prime factors common to both numbers.
     - Here, the common prime factor is \(2\).
     - The lowest power of \(2\) in both factorizations is \(2^3\).

   \[
   \text{GCD}(24, 16) = 2^3 = 8
   \]

### Conclusion:
The greatest amount each notebook can possibly cost is **Php 8.00**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. If another person, Maria, bought the same notebooks for Php 32.00, what is the greatest amount each notebook could cost?
2. How would you determine the least number of notebooks Alicia and Susan could have bought?
3. If the price of the notebooks was Php 4.00 each, how many notebooks did Alicia and Susan buy?
4. What is the smallest amount each notebook could cost if Alicia and Susan bought a different number of notebooks?
5. How does finding the GCD help in solving real-world problems involving divisibility and shared factors?

**Tip:** The Greatest Common Divisor (GCD) is useful in problems where you need to determine the largest possible shared factor, such as finding the largest possible unit price that divides several totals exactly.

Discover how to determine the greatest possible cost of each notebook based on the amounts paid by Alicia and Susan. This problem involves arithmetic and number theory concepts, focusing on finding the Greatest Common Divisor (GCD) of the amounts paid. Suitable for students in Grades 5-7.

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