Question

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

• A. 9
• B. 8
• C. 7
• D. 6

Answer 1

Answer: (A)

Let $S=1!+2!+3!+4!+\dots +11!$
Here, we see that from $4!$ to $11!$, we always get a $12$ factor, so it is always divisible by $12$ .
Now, $1!+2!+3!=1+2+6=9$
Hence, when $S$ is divided by $12$, the remainder is $9$ .