Consider the following statements :

$1.$ $\left(25\right)!+1$ is divisible by $26$

$2.$ $\left(6\right)! +1$ is divisible by $7$

Which of the above statements is/are correct?

How many numbers are there from $14$ to $159$ which are divisible by both $2$ and $8$?

Consider the following two statements :

I. If $n$ is a composite number, then $n$ divides $\left(n-1\right)!$

II. There are infinitely many natural numbers $n$ such that $n^3+2n^2+n$ divides $n!$

Then

Product of four consecutive positive integers is divisible by _____.

Consider the following statements: For any integer $n,$ 

I.. $n^2+3$ is never divisible by $17$ .

II.. $n^2+4$ is never divisible by $17$. Then