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vielfach

Vielfach is a German term that functions as an adverb and, in certain contexts, as an adjective or noun. As an adverb it means “many times” or “repeatedly,” and in more formal usage it can imply “to a great extent.” As an adjective or in compound phrases it indicates plurality or repetition, for example in expressions like vielfach genutzt or vielfache Möglichkeiten, meaning that something is used in many ways or that there are numerous possibilities. In mathematics, das Vielfache refers to a multiple: the value derived from multiplying a base number by an integer.

Etymology and usage context: Vielfach combines viel (much) with the suffix -fach (fold, times), literally forming

In mathematics: The term has a precise technical sense. For a given number n, every number of

See also: Mehrfach, häufig, Vielfaches, Multiplikation.

“many-fold.”
It
is
established
in
standard
German
and
appears
in
both
spoken
and
written
language,
ranging
from
everyday
speech
to
formal
writing.
The
word
often
conveys
emphasis
on
repetition,
abundance,
or
frequency,
and
it
can
replace
less
precise
terms
such
as
häufig
(frequently)
or
mehrfach
(multiple
times
in
a
more
specific
sense)
depending
on
the
register.
the
form
n·k
with
k
as
a
positive
integer
is
a
Vielfache
of
n.
For
example,
12
is
a
Vielfache
of
3
and
of
4,
and
the
set
of
multiples
of
5
is
5,
10,
15,
20,
and
so
on.
The
concept
underpins
the
study
of
divisibility
and
multiples
and
is
taught
in
elementary
number
theory.