there are 15 boys and 10 girls in mrs. lees class she wants to group all of the students so that each grouphas the same number of boy and the same number of girls whats the great number of group's can she have

You need to find the Greatest Common Factor between the 2 numbers:

10: 1, 2, 5, 10

15: 1, 3, 5, 15

The greatest common factor is 5, so they can make 5 Groups

Each group would contain 15/5 = 3 boys and 10/5 = 2 girls.