Question

Suppose the 435 members of the house of representatives are placed on committees consisting of more than 2 members but fewer than 30 member of members and each member is to be on one committees. Each committee is to have an equal number of members and each member is to be on one committee. What size committees are possible?

Answer 1

factors of 435: 5 (87) so five folks one 27 committees. (or 87 folks [not allowed] one 5 committees).

factors of 435: 15 (29) would that work? 15 folks on 29 committees?

Any others?

Answer 2

Suppose the 435 members of the House of Representatives
are placed on committees consisting of more than
2 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.
a. What size committees are possible?
b. How many committees are there of each size?

Answer 3

M = Members.
C = Committees.

3M/C * 145C = 435 Members.
5M/C * 87C = 435.
15M/C * 29C = 435.
29M/C * 15C = 435.

a. 3,5,15,and 29M/C are possible.

b. 145,87,29, and 15C, respectively.