The number at unit place of number 17^123 is :

The correct answer is Option (2) → 3

The unit digit of \(17^{123}\) is the same as the unit digit of \(7^{123}\). The unit digits of the powers of 7 repeat in a cycle of 4:

    \(7^1 = 7\)
    \(7^2 = 49\), unit digit 9
    \(7^3 = 343\), unit digit 3
    \(7^4 = 2401\), unit digit 1

Dividing the power by 4:

    \(123 = 4 \times 30 + 3\)

So \(7^{123}\) has the same unit digit as \(7^3\), which is 3.