Question
florist has 16 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?
bouquets
bouquets
Answers
GPT-4o mini
To determine the greatest number of identical bouquets the florist can make without any leftover flowers, we need to find the greatest common divisor (GCD) of the numbers of tulips and carnations.
The florist has:
- 16 tulips
- 48 carnations
Let's find the GCD of these two numbers.
**Step 1: Prime factorization**
- For 16:
\[
16 = 2^4
\]
- For 48:
\[
48 = 2^4 \times 3^1
\]
**Step 2: Find the GCD**
To find the GCD, we take the lowest power of each prime that appears in the factorization of both numbers.
- For the prime \(2\), the lowest power is \(2^4\).
- For the prime \(3\), it appears only in 48 with a power of \(3^1\) and does not appear in 16.
Thus, the GCD is:
\[
GCD(16, 48) = 2^4 = 16
\]
**Conclusion**
The greatest number of identical bouquets that the florist can make, using all the tulips and carnations without any leftovers, is **16 bouquets**.
The florist has:
- 16 tulips
- 48 carnations
Let's find the GCD of these two numbers.
**Step 1: Prime factorization**
- For 16:
\[
16 = 2^4
\]
- For 48:
\[
48 = 2^4 \times 3^1
\]
**Step 2: Find the GCD**
To find the GCD, we take the lowest power of each prime that appears in the factorization of both numbers.
- For the prime \(2\), the lowest power is \(2^4\).
- For the prime \(3\), it appears only in 48 with a power of \(3^1\) and does not appear in 16.
Thus, the GCD is:
\[
GCD(16, 48) = 2^4 = 16
\]
**Conclusion**
The greatest number of identical bouquets that the florist can make, using all the tulips and carnations without any leftovers, is **16 bouquets**.