Number $36$ has the property that the sum of digits $3+6=9$ is a factor of the product of the digits $3\times 6=18$. Find all two-digit numbers with this property.
So I started by stating the obvious, that numbers $22$, $44$, $66$, and $88$ can work. Then I made an equation: $$(A+B)N=AB,$$ where $N$ can take on different values. I plugged in let’s say $N=1$ and get $A+B=AB$, but this doesn’t really give me any values without guessing and checking. Does anyone know how to solve without guessing and checking values of $A$ and $B$?