Greatest Common Factors
posted by jess .
In the lunch room, 36 fithgraders and 27 fourthgraders 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?

The fifthgraders 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 fourthgraders 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?