$$36={{2}^{2}}\times {{3}^{2}}$$, so the number of its factors would be $$\left( 2+1 \right)\times \left( 2+1 \right)=9$$. But $$\textasciitilde N+2$$ cannot be $$1$$ or $$2$$, so the number of possible values of $$N$$ is$$\textasciitilde9-2=7$$. 
For how many positive integer values of $$N$$ is the expression $$\frac{36}{N+2}$$ an integer? ($$1994$$ AHSME Problem, Question \#$$10$$) 
Options:
[1] $$7$$ 
[2] $$8$$ 
[3] $$9$$ 
[4] $$10$$ 
[5] $$12$$ 