A florist has 18 tulips and 48 carnations. If the florist wants to create identical bouquets without any leftover flowers, what is the greatest number of bouquets the florist can make?


To find the greatest number of identical bouquets the florist can make without any leftover flowers, we need to determine the greatest common divisor (GCD) of the two numbers: 18 tulips and 48 carnations.

### Step 1: Find the prime factors of each number.
- **Prime factorization of 18:**
  - \(18 = 2 \times 3^2\)
- **Prime factorization of 48:**
  - \(48 = 2^4 \times 3\)

### Step 2: Identify the common prime factors with the smallest powers.
- Both 18 and 48 have the prime factors 2 and 3.
- The smallest power of 2 common in both factorizations is \(2^1\).
- The smallest power of 3 common in both factorizations is \(3^1\).

### Step 3: Multiply the common prime factors.
- GCD = \(2^1 \times 3^1 = 2 \times 3 = 6\)

### Conclusion:
The greatest number of identical bouquets the florist can make is **6**.

Would you like any additional details or have any questions?

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Here are five questions related to the problem:
1. How many flowers (tulips and carnations) will be in each bouquet?
2. What is the least number of tulips and carnations in each bouquet if 6 bouquets are made?
3. If the florist had 24 tulips and 60 carnations, what would be the greatest number of bouquets they could make?
4. How does the concept of GCD help in dividing objects into groups without leftovers?
5. Can this method be applied to three different types of flowers? If yes, how?

**Tip:** Understanding the concept of GCD is essential for dividing quantities into equal groups without leftovers.

Discover how to determine the greatest number of identical bouquets that a florist can make with 18 tulips and 48 carnations without any leftover flowers using the concept of Greatest Common Divisor (GCD). Learn the steps involving prime factorization and how GCD helps in dividing quantities into equal groups. Suitable for students in Grades 6-8.

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