# A number theory problem by Akshat Sharda

Given a positive integer $$n$$, let $$P(n)$$ be the product of the nonzero digits of $$n$$.

If $$n$$ has only one digit, then $$P(n)$$ is equal to that digit.

$S = P(1)+ P(2)+\ldots+P(999)$

Find the largest prime factor of $$S$$ ?

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