Question

A P.E. teacher needs to divide 16 male students and 20 female students into teams, each with the same combination of male students and female students and nobody left out. What is the greatest number of teams that can be formed?

Answer 1

I am choosing to solve this way:

If there are 2 teams - both groups are divisible by 2. (8 b & 10 g). That works.

If there are 3 teams - you cannot divide 16 or 20 by 3 evenly.

If there are 4 teams - you can divide into 4 b and 5 g on each team. That works.

5 teams doesn't work because 16/5 would leave one boy left over.

6 teams, doesn't divide equal for boys or girls.

7-10 teams doesn't divide evenly.

2 teams is our greatest number of teams possible.