Question

When $n!+1$ is divided by any natural number between $2$ and $n$ then remainder obtained is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$1$

n! = 1 x 2 x 3 ----- xn
$\to$ i.e, the product of all natural numbers between 2 and n.
$\to$ Hence, it is divisble by all natural numbers between 2 and n.
$\to$ So, when n! is divided by any natural number between 2 and n, the remainder is 0.
$\to$ So, when (n! + 1) is divided by any natural number between 2 and n, the remainder is 1.