# 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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