Question

The remainder obtained when $1!+2!+......100!$ is divided by $240$ is

• A. $153$
• B. $154$
• C. $155$
• D. $156$

Answer 1

The correct option is A $153$

$6!=720$ which is divisible by $240$.

So $6!$ onwards, all the factorials are individually divisible by $240.$

So we have to see from $1!$ to $5!$,

$1!+2!+3!+4!+5!=1+2+6+24+120=153$

So, $153$ when divided by $240$ will give a remainder of $153$
Ans:$153$