BdMO National Secondary 2015/3

[samiul_samin]

Given a positive integer $n$,let $p(n)$ be the product of the non- zero digits of $n$. If $n$ has only one digit then $p(n)=n$.
Let $S=p(1)+p(2)+p(3)+\ldots+p(999)$.What is the largest prime factor of $S$?

[samiul_samin]

Hint

$45+1=46$

Answer

$\fbox {103}$

[samiul_samin]

Source

AIME 1994 Problem 5

Solution

https://artofproblemsolving.com/wiki/in ... /Problem_5

My solution is just same as Solution $2$.So,I am not repeating.