Question

a store owner is arranging clothing on racks. She has 30 sweaters, 45 shirts and 15 pairs of jeans. She wants to put the same number of items on each rack, with only one type of item on each. How many items can she put on a rack?

Answer 1

I think what the teacher wants is 15  which is the greatest common factor of all three numbers and the factors of 15 are 
1 x 15 and 3 x 5 so the she can put one of each, or she can put 3 of each,
 or she can put 5 of each , or she can put 15 of each.

The problem is unclear however because as worded she could put 2 sweaters, 2 shirts and 2 pair of jeans.  I think the teacher wants all the jeans used.  The number 1,3,5 and 15 will use up all of the jeans.
1 jean on 15 racks
or 3 jeans on 5 racks
or 5 jeans on 3 racks
or 15 jeans on one rack

Answer 2

These are the sort of ambiguous word problems 4th graders are exposed to on a daily basis.  As the gentleman mentioned, the teacher expects 15, the largest common factor but 1 on each rack fits as well. It should have read “what’s the maximum number of the same item can he/she place on the racks?”