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Factorial trailing digits

Problem 160

Published on Friday, 7th September 2007, 02:00 pm; Solved by 1773

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)