Question

An event has 9 adults and 27 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. What is the greatest number of tables the planner can set up?

Answer 1

To find the greatest number of tables that can be set up with identical combinations of adults and children, we need to find the greatest common divisor (GCD) of the number of adults and the number of children.

We have:
- Number of adults = 9
- Number of children = 27

We begin by finding the GCD of 9 and 27.

1. **Determine the factors of 9:**
- The factors of 9 are: 1, 3, 9.

2. **Determine the factors of 27:**
- The factors of 27 are: 1, 3, 9, 27.

3. **Identify the common factors:**
- The common factors of 9 and 27 are: 1, 3, 9.

4. **Find the greatest common factor:**
- The greatest common factor among them is 9.

Therefore, the greatest common divisor of 9 and 27 is **9**.

Now, we can calculate the number of tables that can be set up:
- Each table will have:
- \( \frac{9}{9} = 1 \) adult per table,
- \( \frac{27}{9} = 3 \) children per table.

**Conclusion:**

The greatest number of tables the planner can set up is \( \boxed{9} \).