Two-digit number equal to twice its digit product

Exactly one two-digit whole number has the property that multiplying its two digits together gives half of the number itself. Find this number.

36. Writing the number as $10a+b$, the condition $2ab=10a+b$ rearranges to $b=5+\tfrac{5}{2a-1}$. For $b$ to be a single digit we need $2a-1=5$, so $a=3$ and $b=6$; indeed $3\cdot 6=18=36/2$.