Question

a florist has 38 tulips and 19 carnations. if the florist wants to create identical bouquets without any leftover flowers, what is the greatest number of bouquets the florist can make?

Explanation:

Step1: Find GCD of 38 and 19

To find the greatest number of identical bouquets, we need the greatest common divisor (GCD) of 38 and 19. We know that 19 is a factor of 38 (since \(38 = 19\times2\)) and also a factor of itself. So, the GCD of 38 and 19 is 19.

Step2: Confirm the number of bouquets

Since the GCD of the number of tulips (38) and carnations (19) is 19, the florist can make 19 identical bouquets (each bouquet will have \(38\div19 = 2\) tulips and \(19\div19 = 1\) carnation, with no leftovers).

Answer:

19