Multiplication without figures I have taken the 12th problem of this pdf, do you know any way to resolve it without using brute force?
Simply I have to replace '*' of this multiplication below with correct digits, in order to have the factors corrected.
$$\begin{alignedat}{2}*&*4&&\,\times{}\\ &**&&={}\\\hline 44&*4&&  \end{alignedat} $$
Each '*' can be a different digit.

The most straightforward way I can think of is to consider all ten possibilities for the * in 44*4, factor each into primes, and see which ones have prime factors that can recombine into a two-digit number and a three-digit number that ends in a $4$:
$$\begin{align}
4404&=2\cdot2\cdot3\cdot367\\
4414&=2\cdot2207\\
4424&=2\cdot2\cdot2\cdot7\cdot79\\
4434&=2\cdot3\cdot739\\
4444&=2\cdot2\cdot11\cdot101\\
4454&=2\cdot17\cdot131\\
4464&=2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot31\\
4474&=2\cdot2237\\
4484&=2\cdot2\cdot19\cdot59\\
4494&=2\cdot3\cdot7\cdot107
\end{align}$$
There is more than one answer:

 $4444=11\cdot404\qquad 4464=36\cdot124\qquad4494=21\cdot214$

However, this seems a bit brute-forcey. In particular, how do we know $2207$ and $2237$ are primes?  If you're trying to do everything by hand (which I didn't!), you've got your work cut out for you.
