Multiplicative Persistence/Examples/25

Examples of Multiplicative Persistence
$25$ is the smallest positive integer which has a multiplicative persistence of $2$.

Proof
Trivially:

All positive integers between $10$ and $19$ are seen to have a multiplicative persistence of $1$:


 * $1 \times n = n$

where $n$ is a single digit.

Then for 2-digit positive integers starting with $2$:
 * $2 \times n > 9 \implies n > 4$

by inspection.

Hence the result.