Let F=a3+a4+...+an, where ai is the number of faces with degree i. therefore
a3+a4+...+an=8
2E=3a3+4a4+..+ Male
Namely:
24=3a3+4a4+..+ Male
8 = A3+4/3A4+...+N/3A
0 = 8-(a3+a4+...+an) =1/3a4+...+n/3an.
Because ai>= 0, I = 3, ..., N., there must be a4=...=an=0, so a3=8.
In other words, there are eight faces with the number 3.
2. 1400= 2^3*5^2*7
Therefore, the number of positive factors of 1400 is: (3+1) * (2+1) * (1+1) = 24.