A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets. Each bouquet must have an equal number of each type of flower as the other bouquets. What is the largest number of bouquets she can make without having any flowers left over? (1 point)
Responses
36 bouquets
36 bouquets
6 bouquets
6 bouquets
3 bouquets
3 bouquets
9 bouquets
If the florist wants to make bouquets without any flowers left over, the number of each type of flower in each bouquet must be a common factor of 36, 27, and 18.
The common factors of 36, 27, and 18 are 1, 2, 3, 6, and 9.
If the florist wants to maximize the number of bouquets, she must choose the largest common factor.
Therefore, the largest number of bouquets she can make without having any flowers left over is 9 bouquets.
To determine the largest number of bouquets the florist can make without having any flowers left over, we need to find the greatest common divisor (GCD) of the given numbers.
The GCD of 36, 27, and 18 is 9.
Therefore, the largest number of bouquets the florist can make without having any flowers left over is 9 bouquets.
To find the largest number of bouquets the florist can make without having any flowers left over, we need to find the greatest common divisor (GCD) of the numbers of each type of flower she has.
The GCD of 36, 27, and 18 can be found by listing their factors and identifying the largest factor they all have in common:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 27: 1, 3, 9, 27
Factors of 18: 1, 2, 3, 6, 9, 18
From this, we can see that the largest factor they all have in common is 9. Therefore, the largest number of bouquets the florist can make without having any flowers left over is 9 bouquets.