Question

The value of the $0!$ is .

Answer 1

Let's derive the value of the $0!$

As we know,
$5\times 4!=5!$
$\Rightarrow 4!=\frac{5!}{5}$
Similar derivations are depicted in the below table,
As per the above derivations,

$n!=\frac{(n+1)!}{(n+1)}$

Hence, $0!=\frac{1!}{1}=\frac{1}{1}=1$ $(\because 1!=1)$

Therefore, the value of $0!$ is $1.$