2. $\frac{[\sqrt{2013}]+[\sqrt{2014}]+[\sqrt{2015}]+[\sqrt{2016}]}{[\sqrt{2014}] \times[\sqrt{2015}]}$
$=$ ( $[x]$ represents the greatest integer not exceeding the real number $x$).
2. $\frac{1}{11}$.

Notice that, $44^{2}=1936<2013$,
$$
\begin{array}{l}
2016<2025=45^{2} . \\
\text { Then }[\sqrt{2013}]=[\sqrt{2014}]=[\sqrt{2015}] \\
=[\sqrt{2016}]=44 . \\
\text { Therefore, } \frac{[\sqrt{2013}]+[\sqrt{2014}]+[\sqrt{2015}]+[\sqrt{2016}]}{[\sqrt{2014}] \times[\sqrt{2015}]} \\
=\frac{44+44+44+44}{44 \times 44}=\frac{1}{11} .
\end{array}
$$