The last digit of 1213 is :

The correct answer is Option (3) → 2

The last digit of a power of 12 is the last digit of the same power of 2. Powers of 2 end in a cycle of four digits:

    \( \displaystyle 2^1\to 2 \)
    \( \displaystyle 2^2\to 4 \)
    \( \displaystyle 2^3\to 8 \)
    \( \displaystyle 2^4\to 16\to 6 \)
    \( \displaystyle 2^5\to 32\to 2 \)

Dividing the exponent by the cycle length: 13 = 4 × 3 + 1, so the remainder is 1.

    \( \displaystyle 12^{13}\equiv 2^{1}\equiv 2 \pmod{10} \)

The last digit is 2.

Tip: If the remainder on dividing by 4 is 0, take the fourth digit of the cycle (6 for base 2), not the first.