Question

When $1!+2!+3!+.........+25!$ is divided by $7$, what will be the remainder

• A. $0$
• B. $5$
• C. $1$
• D. None of the above

Answer 1

The correct option is B $5$

All numbers after $7!$ will contain $7$

Then, will be divisible by $7$

So, the answer is remainder of $1!+2!+31+4!+5!+6!$

Divided by $7$

$\frac{1+2+6+24+120+720}{7}$

$=\frac{873}{7}$

$=5$ remainder.

Hence, the answer is $5.$