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Factorial

Description

The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

\(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)

The first value of \(n\) for which it's factorial to contain the number 50 is, \(7\)

\(7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040\)


Question

What is the first value of \(n\) for which it's factorial contains the number "082017"?


What is the first value of \(n\) for which it's factorial contains the number "082017"?