What is the difference between "nötig" and "notwendig"? When would one be preferred over the other, or are they always interchangeable?
Is the meaning different?
Looking at the etymology of both adjectives sheds some light on the subtle differences in the meaning of "nötig" *vs. "notwenig":
Are "nötig" or "notwenig" interchangeable?
In most cases "notwenig" can be replaced by "nötig" in contemporary German but "nötig" can not always be replaced by "notwendig". This is mostly the case in colloquial usage, when an an idiomatic expression is involved, as has already been said in conjunction with "haben", or in a more figurative meaning.
There are constructs like
where you can't interchange them. In general
But the latter form is only used as
«Nötig» means that something is essential for a certain purpose («dringend erforderlich» für einen gewissen Zweck) whereas «notwendig» is used if something has to be inevitably present («unvermeidlich, zwangsläufig»; es kann gar nicht anders sein; es liegt in der Natur der Sache).
Although there are some differences in certain situations, those words are interchangeable in most cases.
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In der Mathematik benutzt man nur notwendig .
bedeutet nichts mehr und nichts weniger als:
Beispiel: Damit eine ganze Zahl duch 6 teilbar sei ist es notwendig, dass sie gerade sei.