Question

A choir teacher is dividing 3 sopranos and 12 altos into singing groups. he wants each group to have the same combination of sopranos and altos, with no singers left over. what is the greatest number of groups he can make?

Answer 1

You can have a maximum of 3 groups. This is due to the fact that you only have 3 sopranos to equally divide between groups. Over 3 you would have a group lacking a soprano so 3 is the greatest you can make it.