The least non-negative remainder when 2^75 is divided by 5 will be:-

The correct answer is Option (3) → 3

To find $2^{75} \bmod 5$:

By Fermat’s theorem: $2^{4} \equiv 1 \pmod{5}$

Now, $75 = 4 \cdot 18 + 3$

$\Rightarrow 2^{75} \equiv (2^4)^{18} \cdot 2^3 \equiv 1^{18} \cdot 8 \equiv 8 \pmod{5}$

$8 \bmod 5 = 3$

Answer: 3