Multiplicative Persistence/Examples/679

Examples of Multiplicative Persistence

$679$ is the smallest positive integer which has a multiplicative persistence of $5$.

We have:

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

$\ds 6 \times 7 \times 9$

$=$

$\ds 378$

$\text {(2)}: \quad$

$\ds 3 \times 7 \times 8$

$=$

$\ds 168$

$\text {(3)}: \quad$

$\ds 1 \times 6 \times 8$

$=$

$\ds 48$

$\text {(4)}: \quad$

$\ds 4 \times 8$

$=$

$\ds 32$

$\text {(5)}: \quad$

$\ds 3 \times 2$

$=$

$\ds 6$

The fact that it is the smallest can be demonstrated by brute-force methods.

$\blacksquare$

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $679$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $679$