Question

if 2*2*2.........1000 times is divided by 5,then what will be thr remainder??

Answer 1

have you considered fermat's little theorem

Answer 2

no

Answer 3

There is no remainder, it would equal 400 I think.

Answer 4

Using @freckles 's hint: \[2^{1000}=\left(2^{20}\right)^5\equiv2^{20}\mod5\]
\[2^{20}=\left(2^4\right)^5\equiv 2^4\mod5\]
In other words, the remainder of \(2^{1000}\) divided by \(5\) is the same as the remainder of \(2^4\) divided by \(5\).