The museum’s show for July features 30 oil paintings by different artists. All artists show the same number of paintings and each artist shows more than 1 painting. How many artists could be featured in the show?

Answer: We have many options:

1) 15 artists, with 2 paintings per artist.

2) 10 artists, with 3 paintings per artist.

3) 6 artists, with 5 paintings per artist.

4) 5 artists, with 6 paintings per artist.

5) 3 artists, with 10 paintings per artist.

6) 2 artists, with 15 paintings per artist.

by different artists, then the number of artists must be more than 1.

each artist shows more than 1 painting: >1 painting/artist

(30 oil paintings)/(2 paintings/artist)=15 artists

(30 oil paintings)/(3 paintings/artist)=10 artists

(30 oil paintings)/(5 paintings/artist)=6 artists

(30 oil paintings)/(6 paintings/artist)=5 artists

(30 oil paintings)/(10 paintings/artist)=3 artists

(30 oil paintings)/(15 paintings/artist)=2 artists

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