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
16
8
96
12
To find the largest number of bouquets she can make without having any flowers left over, we need to find the greatest common divisor (GCD) of 48, 32, and 16.
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.
To find the GCD, we take the smallest exponent for each prime factor that appears in all three numbers: 2^4.
Therefore, the largest number of bouquets she can make without having any flowers left over is 16.