AHSME 1995 Problem 29

For how many three-element sets of distinct positive integers $\{a,b,c\}$ is it true that $a \times b \times c = 2310$?

$\mathrm{(A) \ 32 } \mathrm{(B) \ 36 } \mathrm{(C) \ 40 } \mathrm{(D) \ 43 } \mathrm{(E) \ 45 }$