If there were 64 sixth graders, list all of the ways they could have been divided equally into groups of 10 or fewer students?

Question

Nova Allen · Accepted Answer

There are four ways in which sixth graders could have been divided equally into groups of #10# or fewer students.

We have #64# sixth graders. Let us write the group sizes of #10# or fewer size in which they can be divided equally starting from #1# in increasing order in a column (these will be obviously factors of #64#) and then against them, let us write the number of groups. The result is as follows: #Number# #of# #groupscolor(white)(XXXXXX)Group# #Size# #color(white)(XX)1color(white)(XXXXXXXXXXXXXXX)64# #color(white)(XX)2color(white)(XXXXXXXXXXXXXXX)32# #color(white)(XX)4color(white)(XXXXXXXXXXXXXXX)16# #color(white)(XX)8color(white)(XXXXXXXXXxxXXXXX)8# As next number can only be #16#, which is greater than #0#, we stop here. Hence There are four ways in which sixth graders could have been divided equally into groups of #10# or fewer students.

Gianna Caruso · Answer

undefined To determine all the ways 64 sixth graders could be divided equally into groups of 10 or fewer students, we can use basic division.

Here are the possible divisions:

1. 6 groups of 10 students each.
2. 7 groups of 9 students each, with 1 student left over.
3. 8 groups of 8 students each.
4. 9 groups of 7 students each, with 1 student left over.
5. 10 groups of 6 students each, with 4 students left over.

These are all the possible ways to divide 64 sixth graders into groups of 10 or fewer students, ensuring equal distribution.