The least non-negative remainder when 64 x 65 x 66 is divided by 67, is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 61
Modulo 67, each factor is a small negative number: \( 64\equiv -3 \), \( 65\equiv -2 \) and \( 66\equiv -1 \).
\( 64\times 65\times 66\equiv(-3)(-2)(-1)\ (\mathrm{mod}\ 67) \)
\( \equiv -6\ (\mathrm{mod}\ 67) \)
\( \equiv 67-6=61\ (\mathrm{mod}\ 67) \)
So the least non-negative remainder is 61.