The remainder, when 271 × 373 × 575 × 429 is divided by 4, is:

The correct answer is Option (2) → 1

The remainder of a product equals the remainder of the product of the individual remainders. Only the last two digits matter for division by 4:

    \( \displaystyle 271\equiv 71\equiv 3 \)
    \( \displaystyle 373\equiv 73\equiv 1 \)
    \( \displaystyle 575\equiv 75\equiv 3 \)
    \( \displaystyle 429\equiv 29\equiv 1\ \pmod 4 \)

    \( \displaystyle 3\times 1\times 3\times 1=9\equiv 1\pmod 4 \)

So the remainder is 1.

Shortcut: Write 3 ≡ −1 (mod 4): the product is \( (-1)(1)(-1)(1)=1 \).