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