Question

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

• A. $9$
• B. $8$
• C. $7$
• D. $6$

Answer 1

The correct option is A $9$

Given that: $1!+2!+3!+4!+...........+11!$

$=(1!+2!+3!)+(4!+5!+......+11!)$

$=(1+2+6)+(4!+5!+........+11!)$

$=9+(4!+5!+.......+11!)$

$4!,5!,........11!$ are divisible by $12$

So when you will divide given expression by $12$ the remainder will be $9$