Ahigh school swim team has 12 new female swimmers and 30 returning female swimmers. each practice team must have the same number of new a returning female swimmers.
a) what is the greatest number of practice teams the coach can make using every swimmer?
b) how many new and returning female swimmers will be on each practice team?

What we have to do is to find the largest common divisor of the two numbers: 12 and 30. It must be at least 2, since they're both even, and at least 3 since both are divisible by 3, so that means that it it also must be at least 6 (2*3=6; if they're divisible by 2 and 3, they must be both divisible by 6).

But they have no bigger divisor than this.

So that means that the number of groups will be 6 (both groups can be divided into 6). It will have 2 (12/6=2) newcomers and 5 (30/6=5)  advanced swimmers.