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Factorial Trailing Digits

 Published on Friday, 7th September 2007, 02:00 pm; Solved by 3758;
Difficulty rating: 60%

Problem 160

For any $N$, let $f(N)$ be the last five digits before the trailing zeroes in $N!$.
For example,

  • $9! = 362880$ so $f(9)=36288$
  • $10! = 3628800$ so $f(10)=36288$
  • $20! = 2432902008176640000$ so $f(20)=17664$

Find $f(1\,000\,000\,000\,000)$.