Question

Can we have any n £ n , where 7power n ends with the digits zero

Answer 1

let , if possible 7^n ends with digits zero

As 7^n ends with digit zero
=> 7^n must have factor 2 and 5 ----(i)

but according to fundamental theorem of arithmetic, it gaurantees that 7 ^n can have only factor as multiple of 7 ----(ii)

(i) and (ii) contradicts each other
Thus 7^n can never end with digit zero for any natural number n...

Answer 2

According to given sum,

$\: {7}^{n} \: doesnot \: end \: with \: the \: digit \: zero.$

If it ends with a digit zero. Then, the number must have 2 & 5 as factors.

But the number 7 won't have factors 2 & 5 .

$hence \: {7}^{n} \: doesnot \: ends \: with \: 0.$

:-)Hope it helps u.