Question

The remainder obtained when $1!+2!+3!+\dots \dots +95!$ is divided by $15$ is

• A. $3$
• B. $14$
• C. $1$
• D. none of the above

Answer 1

The correct option is A $3$

From $5!$ to $95!$ every factorials contains $5$ and $3$

$5!=5\times 4\times 3\times 2\times 1$

$\therefore 5!$ to $95!$ is a multiple of $15$

$5=1!+2!+3!+4!+5!+.....+95!$

$\frac{5}{15}=\frac{33}{15}+\frac{5!}{15}..+\frac{95!}{15}$

$\frac{33}{15}\to$ Remainder will be $3$