Throughout the year, a graduate professor wants her students to work in as many distinct groups of a consistent size as possible. If she has a total of 8 students, how many students should she place in each group?

3

4

5

6

7

What I do not understand here is for example how for 3 it was solved. It took the number of groups of 3 you can form from the 8 students, but there are 8 in total, if we were to have groups of 3, then you can get two groups of three and one group of two, so in the next one these 2 have to stay together and then how many of the six can make groups of 3. Am I missing something here?