Problem 18 (1989 AJHSME)

Many calculators have a reciprocal key $\frac{1}{x}$ that replaces the current number displayed with its reciprocal. For example, if the display is $00004$ and the key is depressed, then the display becomes $000.25$. If $00032$ is currently displayed, what is the fewest number of times you must depress the $\frac{1}{x}$ key so the display again reads $00032$?