The least non-negative remainder when 2^101 is divided by 5 is:

The correct answer is Option (3) → 2

Since \(2^4 = 16 = 3 \times 5 + 1\),

    \(2^4 \equiv 1 \pmod 5\)

Write the exponent as a multiple of 4 plus a remainder, \(101 = 4 \times 25 + 1\):

    \(2^{101} = \left(2^4\right)^{25} \cdot 2 \equiv 1^{25} \cdot 2 = 2 \pmod 5\)

So the remainder is 2.