The remainder when 52 × 67 × 83 is divided by 5 is

The correct answer is Option (3) → 2

In modulo arithmetic each factor may be replaced by its remainder before multiplying.

    \(52 \equiv 2 \pmod{5}\)
    \(67 \equiv 2 \pmod{5}\)
    \(83 \equiv 3 \pmod{5}\)

    \(52 \times 67 \times 83 \equiv 2 \times 2 \times 3 = 12 \pmod{5}\)

    \(12 = 5 \times 2 + 2\)

So the remainder is 2.