A florist has 48 roses, 32 tulips, and 16 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? PAR 6.2
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1 point
16
8
96
12
To determine the largest number of bouquets she can make without having any flowers left over, we need to find the greatest common divisor (GCD) of the number of roses, tulips, and carnations.
The prime factorization of 48 is 2^4 * 3.
The prime factorization of 32 is 2^5.
The prime factorization of 16 is 2^4.
The GCD of these numbers is 2^4, which is 16.
Therefore, the florist can make 16 bouquets without having any flowers left over.
The correct answer is 16.
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 number of each type of flowers.
The GCD of 48, 32, and 16 is 16.
Therefore, the florist can make a maximum of 16 bouquets without having any flowers left over.
To find the largest number of bouquets the florist can make without any flowers left over, we need to find the greatest common divisor (GCD) of the numbers of each type of flower - roses, tulips, and carnations.
The GCD will give us the maximum number of bouquets we can make while using an equal number of each type of flower.
To find the GCD, we can use the prime factorization method. Let's start by finding the prime factorization of each number:
48 = 2^4 * 3
32 = 2^5
16 = 2^4
Next, we find the least exponent for each common prime factor:
2^4 * 3 (for 48)
2^5 (for 32)
2^4 (for 16)
Finally, we multiply these common prime factors together:
2^4 * 3 = 16 * 3 = 48
Therefore, the largest number of bouquets the florist can make without having any flowers left over is 48.