The value of 6^10 mod 5 is :

The correct answer is Option (3) → 1

Since 6 = 5 + 1, the remainder of 6 on division by 5 is 1:

    \(6 \equiv 1 \pmod{5}\)

Powers keep the congruence, so

    \(6^{10} \equiv 1^{10} = 1 \pmod{5}\)

So \(6^{10}\) mod 5 = 1. (A remainder on division by 5 is always 0, 1, 2, 3 or 4, so 5 is never possible.)