a math teacher and a science teacher combine their first- period classes fora group activity. the math class has 24 students and the science class has 16 students. the teachers need to divide the students into groups of the same size. eatch group must have the same number of math students. find the greatest number of groups possible.

Question

loser66 · Answer

find g.c.d(24, 16) , that is the answer.

anonymous · Answer

i need to show work how do i set it up @Loser66

loser66 · Answer

Ok, let do elementary step
16 = 1*16 and 24 =1*24, so that this is the first possibility to have the "same" number of math students,( because we have no other group to compare)
16 = 2*8 
if we have 2 science groups, each has 8 students, so that 24 math student must be divided by 2 to get 12 students / group, right? That is the second case
if we have 8science groups, each has 2 students, so that 24 math students must be divided by 8, which means 3students/ group. And all groups have the same math students

loser66 · Answer

16= 4*4
that means we divide 16 science students into 4 groups, each group has 4students.
So?? Math group must be divided by 4 also, and each group will have 24$\div$ 4= 6 students , that is the 4th case

loser66 · Answer

and that 's it, just 4 ways to get the required group

anonymous · Answer

soo witch one do i write ?

loser66 · Answer

And the greatest of group is the case 8 groups, each has 2 science students + 3 math students

loser66 · Answer

Write all. Have to prove why you choose 8 groups.