A number theory problem by Christopher Boo

Number Theory Level 1

For any positive integer $n$ , the following is true:

$n$ is divisible by $1.$
$n(n+1)$ is divisible by $1\times 2.$
$n(n+1)(n+2)$ is divisible by $1\times 2\times 3.$

Is it true that $n(n+1)(n+2)(n+3)$ must be divisible by $1\times 2 \times 3\times 4?$