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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 :)

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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?

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    The full question is just like i wrote. I can not guess anything. Still searching in google – 2017-01-16
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    The symbol $m|n$ means that $m$ is a divisor of $n$. This relation is a partial ordering on $\Bbb N$. We can speak about minimal (maximal) elements only if some partial ordering is given. For the usual ordering by the $\le$ relation everything is clear. But there are the other quite natural orderings like divisibillity, inclusion of sets etc. Here some additional properties hold. In particular, not every two elements are comparable. Observe that any two distinct primes are not comparable wrt. divisibility relation. The same with any two coprime numbers (which GCD is $1$). – 2017-01-16
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    thank you for explanation . thats realy clear for me now – 2017-01-16
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Hint: $1\mid n$ and $n\mid 0$ for every natural number $n$.

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    About the maximal element the answer depends on whether or not $0$ is a natural number. This is a convention. I work with $0\not\in\Bbb N$. :-) – 2017-01-16
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    @szw1710 That's why I didn't gave a name to the relation of divisibility in the first place. I just wanted to give a hint to the OP so that he/she concluded the argument according with his/her convention. – 2017-01-16
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    I gave also my hint in a similar form. BTW, as an experienced user, please tell me if hints are preferred than full solutions (in answers, not in comments). Maybe this depends on a person who answers the question. – 2017-01-16
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    @szw1710 Not that experienced but... Sometimes the OP just asks for some hint or pointer and in that case giving a full answer might be too much (for those cases the hidden boxes sometimes are useful in order to not spoil the answer for the OP). As for giving a hint instead of a full answer when no preference was specified, it is up to you (provided it is a useful hint). My rule of thumb is to give a hint if I feel that the OP won't (or shouldn't) have a problem filling the details. – 2017-01-16