There are 638 students at a museum. All the students will tour the museum in groups of up to 6 students. What is the smallest number of tour groups that can be used?

First, divide 638 but 6 the best you can having remaining numbers
     106                                               1.) divide
 6 | 638
   - 636                                              2.) subtract

There are 2 remaining students ( and yes every student must have a group)
So you have to create a another group for these 2 students making there be

107 tour groups