Numerical rebus Given:
${AA}\times{BC}=BDDB$
Find $BDDB$:


*

*$1221$

*$3663$

*$4884$

*$2112$


The way I solved it:
First step - expansion & dividing by constant ($11$):
$AA\times{BC}$=$11A\times{BC}$


*

*$1221$ => $1221\div11$ => $111$

*$3663$ => $3663\div11$ => $333$

*$4884$ => $4884\div11$ => $444$

*$2112$ => $2112\div11$ => $192$


Second step - each result is now equal to $A\times{BC}$. We're choosing multipliers $A$ and $BC$ manually and in accordance with initial condition. It takes a lot of time to pick up a number and check whether it can be a multiplier.
That way I get two pairs:
$22*96$=$2112$
$99*37$=$3663$
Of course $99*37$=$3663$ is the right one.
Is there more efficient way to do this? Am I missing something?
 A: I'm not sure what you mean by "pick up a number and check whether it can be a multiplier".
You can factorize the numbers $111$, $333$, $444$, $192$:
$$
\begin{align}
111&=3\cdot37\;,\\
333&=3^2\cdot37\;,\\
444&=2^2\cdot3\cdot37\;,\\
192&=2^6\cdot3\;.
\end{align}
$$
From these factorizations it's straightforward to find the factorizations into one single-digit and one double-digit number:
$$
111=3\cdot37\;,\\
333=9\cdot37\;,\\
444=6\cdot74\;,\\
192=2\cdot96\;,\\
192=3\cdot64\;,\\
192=4\cdot48\;,\\
192=6\cdot32\;,\\
192=8\cdot24\;.
$$
A: I think your division by $11$ is a good first step.  Now maybe you know $111=3 \cdot 37$ and that is the key to factoring three of your four choices.  Note that now you need a single digit $A$ times a two digit $BC$, so $333=9\cdot 37$ and $444=6 \cdot 74$ are the only acceptable ones and should be quick to find from the first.  For $333$ you have to add in a factor $3$ and $3 \cdot 37$ has three digits, so it has to pair with the $3$.  For $444$, you need to add in a factor $4$ and neither number can take the whole thing, so they have to share.  Your possibilities are $33\cdot 37=1221, 99 \cdot 37=3663, 66 \cdot 74=4884$.  Seeing that the second works, we are done.
Alternately, you might just notice that $3663+37=3700$, too big a coincidence to ignore and say $3663=(100-1)37$
