18. A five-digit number $A B C D E$ is a multiple of 2014, and $C D E$ has exactly 16 factors. What is the smallest value of $A B C D E$?
【Answer】 24168
Analysis: For extremum problems, start from the extreme situation. The smallest number that is both a five-digit number and a multiple of 2014 is 10070; the application of the number of divisors, $16=16=8 \times 2=4 \times 4=4 \times 2 \times 2=2 \times 2 \times 2 \times 2$, after decomposing into prime factors, the exponents could be $(15),(7,1)$
\begin{tabular}{|c|c|}
\hline 10070 & $70=2 \times 5 \times 7$, discard \\
\hline 12084 & $84=2^{2} \times 3 \times 7$, discard \\
\hline 14098 & $98=2 \times 7^{2}$, discard \\
\hline 16112 & $112=2^{4} \times 7$, discard \\
\hline 18126 & $126=2 \times 3^{2} \times 7$, discard \\
\hline 20140 & $140=2^{2} \times 5 \times 7$, discard \\
\hline 22154 & $154=2 \times 7 \times 11$, discard \\
\hline 24168 & $168=2^{3} \times 3 \times 7$, fits \\
\hline
\end{tabular}