Question

Consider the number $4^n$, where n is a natural number. Check whether there is any value of n $ϵ$ N for which $4^n$ ends with the digit 0.

Answer 1

Let us first consider an example of a number which ends with the digit zero.

$10=5$ x $2$

$20=2$ x $2$ x $5$

$50=2$ x $5$ x $5$

Here we note that the numbers with $0$ has both $2$ and $5$ as their prime factors.

but in this question $4^n$ $=$ ${(2\times 2)}^n$

This does not have the $5$ as prime factor, So it does not end with zero.

Therefore we can conclude that $4^n$ cannot end with zero for any natural number $n$