this is a sentence in a textbook which said:

Der Bahndrehimpuls L eines Elektrons ist ein ganzzahliges Vielfache von ...

Leaving aside the technical thing, I would like to know how ein ganzzahliges Vielfache works grammatically, as if we treat vielfache as an adjective, which seems incorrect because its ending should be consistent with ganzzahliges

Source: Physik Abitur - Basiswissen Schule - DUDEN

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  • 5
    It is a typo / error. I has to read ein ganzzahliges Vielfaches.
    – Jonathan Herrera
    Jul 15, 2022 at 14:29
  • 1
    I can haz t, pleaze? Jul 15, 2022 at 19:14
  • @userunknown hmmm, what do u mean
    – Le Nguyen
    Jul 16, 2022 at 3:25
  • 1
    @LeNguyen: "It has to read ..." - oder vielleicht aber auch "I have to read ...". Nicht wichtig, nur leicht kurios, einen Typo mit einem Typo (wenn es denn ein Typo war) zu kritisieren. Jul 16, 2022 at 18:30
  • 1
    ganzzahliges Vielfaches = integer multiple
    – Paul Frost
    Jul 19, 2022 at 23:10

1 Answer 1


As Jonathan Scholbach already mentioned, there's a typo, it needs to be

... ein ganzzahliges Vielfaches von ...

In this case, "Vielfaches" is a noun, which would translate to "multiple", as in

The second number was a multiple of the first.

In this case, it isn't just any multiple, but the factor has to be an integer. In German, the set of integers ℤ is called the ganze Zahlen, literally the "whole numbers" (because there's no fractional part).

So, a "ganzzahliges Vielfaches" is a multiple where the factor is an integer. The Bahndrehimpuls could, according to the quote in the question, for example be 2 * (h/2*pi), or 35 * (h/2*pi), or -7 * (h/2*pi), but not 3.8 * (h/2*pi).

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