What are the maximal and minimal element?

Question

What are the maximal and minimal elements, if any, of the set, N, of all natural numbers under divisibility? Is there a minimum or maximum element?

I feel hard to understand that question ...

Honestly I was so far away this topic . I hardly understand and thanks to you in advance. I need a clear explanation :)

Answer 1

The divisibility relation is a partial ordering of $\Bbb N$: $m\prec n\iff m|n$. Because $1$ is a divisor of everything natural, then $1$ is a minimal element in this ordering. Moreover, this is the least element (because $1\prec n$ for any $n\in\Bbb N$).

Concerning a possible maximal element consider a hint: is there $m\in\Bbb N$ s.t. $m$ is not a predecessor of any natural number $n$? What does it mean?

Answer 2

Hint: $1\mid n$ and $n\mid 0$ for every natural number $n$.