The least non-negative remainder when 3^200 is divided by 8 is :

The correct answer is Option (4) → 1

A small power of 3 already leaves remainder 1 on division by 8:

    \( \displaystyle 3^2=9\equiv 1\pmod 8 \)

Then

    \( \displaystyle 3^{200}=\left(3^2\right)^{100} \)

    \( \displaystyle \equiv 1^{100}=1\pmod 8 \)

So the least non-negative remainder is 1.