Homework Help: Greatest Common Factors

Posted by jess on Tuesday, September 16, 2008 at 10:38pm.

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?

Greatest Common Factors - TN, Tuesday, September 16, 2008 at 11:03pm
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?

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