Factorials

The factorial of an integer $n$, denoted as $n!$, is the product of all integers from $1$ to $n$ inclusive. Factorials grow rapidly: for example, $13!$ is already too large to be stored in a $32$-bit integer variable on most computers, and $70!$ is too large for most floating-point variables. Your task is to find the rightmost non-zero digit of $n!$. For example, 5! = 1 \times 2 \times 3 \times 4 \times 5 = 120, so the rightmost non-zero digit for $5!$ is $2$. Also, 7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 = 5040, so for $7!$ the answer is $4$.