In the lunch room, 36 fith-graders and 27 fourth-graders are sitting in equal groups. All the students in each group are in the same grade.What is the greatest number of students who could be in each group?

Answer 1

The fifth-graders could evenly be in
1 group of 36 ... or
2 groups of 18 ...or
3 groups of 12 ... or
4 groups of 9 ... or
6 groups of 6 ... or
9 groups of 4 ...or
12 groups of 3 ... or
18 groups of 2 ... or
36 groups of 1

The fourth-graders could evenly be in
1 group of 27...or
3 groups of 9...or
9 groups of 3...or
27 groups of 1
If they have to have the same number in both groups, they could either have 1, 3 or 9 (the common factors). Since we want the greatest number, which would we choose?