even vs odd

True or False?

If we remove the trailing zeroes of the factorial \(n!,\) where \(n\) is a positive integer such that \(5 \leq n < 10,\) then the last digit of the remaining number is even. This is still true for all \(n \ge 10.\)

\(\)
Hints:

  • \(5! = 120 \longrightarrow 12 \longrightarrow 2\) is even.
  • \(10! = 3628800 \longrightarrow 36288 \longrightarrow 8\) is even.
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