Multiplicative Persistence/Examples/10

Examples of Multiplicative Persistence

$10$ is the smallest positive integer which has a multiplicative persistence of $1$.

Proof

Trivially:

\(\text {(1)}: \quad\)

\(\ds 1 \times 0\)

\(=\)

\(\ds 0\)

All positive integers less than $10$ are already single digits and so have a multiplicative persistence of $0$.

$\blacksquare$