Question

The remainder obtained when $64\times 65\times 66$ is divided by $67$, is

• A. $60$
• B. $62$
• C. $61$
• D. $63$

Answer 1

Answer: (C)

$64\equiv -3$ Mod $(67)$
$65\equiv -2$ Mod $(67);66=-1$ Mod $(67)$
$\therefore 64\times 65\times 66=(-3)(-2)(-1)$ Mod $(67)$
$=-6$ Mod ($67)=61$ Mod $(67)$
$\therefore$ Required remainder is $61$.