An artist had 45 pieces of turquoise and 60 cat's eye marbles.each sculpture she made contained the same number of each kind of stone and more than one of each. What is the greatest number of sculptures she could have made ?

The way I read this, a sculpture with the least material would be 2T and 2M, T being tourquoise and M being marbles

So she could make 21 of these minimum's plus one of 3T ,3M
using 45 T's and 45 M's

for a maximum of 22 sculptures.

To find the greatest number of sculptures the artist could have made, we need to find the common factors of 45 and 60 and choose the largest one.

Step 1: Find the factors of 45.
The factors of 45 are 1, 3, 5, 9, 15, and 45.

Step 2: Find the factors of 60.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Step 3: Identify the common factors.
The common factors of 45 and 60 are 1, 3, 5, 15.

Step 4: Choose the largest common factor.
The greatest common factor of 45 and 60 is 15.

Therefore, the artist could have made a maximum of 15 sculptures, with each sculpture containing 15 pieces of turquoise and 15 cat's eye marbles.