Question

The remainder obtained when $1!+2!+......49!$ is divided by $20$ is

• A. $13$
• B. $33$
• C. $12$
• D. $11$

Answer 1

The correct option is A $13$

The value of $5!$ is $120$
All the factorials after $5!$ will leave remainder zero when divided by 20

So the remainder can be calculated by calculating the remainder of

$\frac{(1!+2!+3!+4!)}{20}=\frac{(1+2+6+24)}{20}=\frac{33}{20}$
$\therefore$ Remainder is $13$.