Question

The remainder obtained when $1!+2!+3!+\cdots +11!$ is divided by $12$ is

• A. $9$
• B. $8$
• C. $7$
• D. $6$

Answer 1

The correct option is A $9$

We observe that $k!$ is divisible by $12$ for $k\ge 4,$ hence leaves remainder $0$ when $k!(k\ge 4)$ is divided by $12.$
$\therefore$ The remainder when the sum $1!+2!+3!=9$ is divided by $12$ is $9$.