Suppose the 435 members of the House of Representatives are placed on committees consisting of more than2 members but fewer than 30 members. Each committee is to have an equal number of members and each member is to be on only one committee.

Question

a. What size committees are possible?
b. How many committees are there of each size?

Answer 1

The number of members in each committee must divide 435.
So let's us factorize 435 to get:
435=3*5*29
So the possible committee sizes are 3, 5 and 29.
Finally, divide 435 by the committee size to get the number of committees corresponding to each size.