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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Updated on: 10-Oct-2022

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