Question

For a dinner party, Malia is creating individual servings of appetizers. She has 8 carrot sticks and 12 celery sticks. If she wants each serving to be identical, with no food left over, what is the greatest number of servings Malia can create?

Answer 1

To find the greatest number of servings Malia can create with 8 carrot sticks and 12 celery sticks, we need to determine the greatest common divisor (GCD) of the two quantities.

1. **List the factors of each number**:
- Factors of \(8\): \(1, 2, 4, 8\)
- Factors of \(12\): \(1, 2, 3, 4, 6, 12\)

2. **Identify the common factors**:
- The common factors of \(8\) and \(12\) are \(1, 2, 4\).

3. **Find the greatest common factor**:
- The greatest common factor is \(4\).

So, the greatest number of identical servings Malia can create, with no food left over, is \( \boxed{4} \).

4. **Verify**:
- If there are \(4\) servings, each serving will have:
- Carrot sticks: \( \frac{8}{4} = 2\) carrot sticks
- Celery sticks: \( \frac{12}{4} = 3\) celery sticks

5. **Check for no leftovers**:
- \(4\) servings of \(2\) carrot sticks use \(4 \times 2 = 8\) carrot sticks (all used).
- \(4\) servings of \(3\) celery sticks use \(4 \times 3 = 12\) celery sticks (all used).

Thus, Malia can create \( \boxed{4} \) servings without any leftovers.