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Examine whether $(21)^n$ can end with the digit 0 for any $n\in N$.
Given :
The given number term is $21^n$.
To do :
We have to check whether $(21)^n$ can end with the digit 0 for any $n\in N$.
Solution :
If a number ends with the digit 0, it should have both 2 and 5 as it's prime factors.
$21^n$
$21 = 3\times 7$
$21^n= (3\times 7)^n = 3^n \times 7^n $
So, $21^n$ has 3 and 7 as it's prime factors but not 2 and 5.
Therefore, it can be concluded that $(21)^n$ cannot end with the digit 0 for any $n\in N$
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