A florist has 12 sunflowers and 54 tulips. The florist plans to make as many identical arrangements with the flowers as possible with no flowers left over. What is the greatest number of arrangements the florist can make?

4 number of maximum arrangements.

Step-by-step explanation:

Number of sunflowers available = 12

Number of tulips available = 54

To find:

Number of identical arrangements possible with flowers such that no flowers are left over.

Solution:

To find such arrangements, we have to find the Highest Common Factor, according to which we will be able to divide them as per the requirement.

First of all, let us factorize both the given numbers:

12 = 2 2 3

54 = 2 3 3 3

The common factors are 1, 2, 3 and 6.

So, if we keep 6 rows, then we can have = 2 number of sunflowers in each row and = 9 number of tulips in each row.

If we keep 3 rows, then we can have = 4 number of sunflowers in each row and = 18 number of tulips in each row.

If we keep 2 rows, then we can have = 6 number of sunflowers in each row and = 27 number of tulips in each row.

If we keep 1 row, then we can have 12 number of sunflowers in each row and 54 number of tulips in each row.

a negative exponent is translated as follows:

so, we have