even vs odd

True or False?

If we remove the trailing zeroes of the factorial n!,n!, where nn is a positive integer such that 5n<10,5 \leq n < 10, then the last digit of the remaining number is even. This is still true for all n10.n \ge 10.


Hints:

  • 5!=1201225! = 120 \longrightarrow 12 \longrightarrow 2 is even.
  • 10!=362880036288810! = 3628800 \longrightarrow 36288 \longrightarrow 8 is even.
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