Question
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A florist has an order to make flower bouquets. The order calls for the use of 45 roses and 63 carnations. Each bouquet made will need to be the same.
If all of the flowers are to be used, there can be at most
bouquets made from the flowers requested in the order.
Submit
5
7
5T.6
200m
ヒ
A florist has an order to make flower bouquets. The order calls for the use of 45 roses and 63 carnations. Each bouquet made will need to be the same.
If all of the flowers are to be used, there can be at most
bouquets made from the flowers requested in the order.
Submit
5
7
5T.6
200m
ヒ
Answers
GPT-4o mini
To determine the maximum number of bouquets that can be made from 45 roses and 63 carnations, we need to find the greatest common divisor (GCD) of the two numbers.
1. **Find the GCD of 45 and 63:**
- The prime factorization of 45 is \(3^2 \times 5^1\).
- The prime factorization of 63 is \(3^2 \times 7^1\).
- The common factors are \(3^2\).
- Therefore, the GCD is \(9\).
2. **Calculate the maximum number of bouquets:**
- Since we need equal amounts of each flower in every bouquet, the maximum number of bouquets is determined by the GCD:
- Thus, \( \text{maximum bouquets} = GCD(45, 63) = 9\).
The correct answer is not listed in the options provided. However, the correct maximum number of bouquets that can be made is **9**.
1. **Find the GCD of 45 and 63:**
- The prime factorization of 45 is \(3^2 \times 5^1\).
- The prime factorization of 63 is \(3^2 \times 7^1\).
- The common factors are \(3^2\).
- Therefore, the GCD is \(9\).
2. **Calculate the maximum number of bouquets:**
- Since we need equal amounts of each flower in every bouquet, the maximum number of bouquets is determined by the GCD:
- Thus, \( \text{maximum bouquets} = GCD(45, 63) = 9\).
The correct answer is not listed in the options provided. However, the correct maximum number of bouquets that can be made is **9**.