Express $404$ as a product of primes.

Three sets of English,Hindi,and Mathematics books have to be stacked in such a way that all the books are stored topic-wise and the height of each stack is the same. The number of English books is $96$,the number of Hindi books is $240$,and the number of Mathematics books is $336$. Assuming that the books are of the same thickness,determine the number of stacks of English,Hindi,and Mathematics books.

$L.C.M.(115, 25) = \ldots$

Prove that $n^{2}-n$ is divisible by $2$ for every positive integer $n$.

Show that $12^{n}$ cannot end with the digit $0$ or $5$ for any natural number $n$.

"The product of two consecutive positive integers is divisible by $2$." Is this statement true or false? Give reasons.