Question

The remainder when $1!+2!+3!+4!+......+100!$ is divided by $240$ is?

• A. $153$
• B. $33$
• C. $73$
• D. $187$

Answer 1

The correct option is A

$153$

Find the remainder

We know that, $6!=720$ is divided by $240$

Before $6!$ no factorials are divisible by $240$

Now,

$\underset{n=1}{\overset{5}{\sum n!}}$ $=1!+2!+3!+4!+5!$

$$\begin{gathered} =1+2+6+24+120 \\ =153 \end{gathered}$$

Hence, the correct option is $\left(\mathrm{A}\right)$