
vielfach
often
Used adverbially: often, many times, on many occasions.
Dieses Problem wurde bereits vielfach diskutiert.
This problem has already been discussed often.
often / multiple
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often
Used adverbially: often, many times, on many occasions.
Dieses Problem wurde bereits vielfach diskutiert.
This problem has already been discussed often.

multiple
Used adjectivally: present in large number or variety; multiple.
Auf vielfachen Wunsch wird das Konzert wiederholt.
Due to multiple requests, the concert will be repeated.
The word consists of 'viel' (much / many) and the ending '-fach'. This ending means '-mal' (times) or '-fältig' (-fold), as in 'einfach' (simple / single) or 'zweifach' (double / twofold). 'Vielfach' (often / multiple) therefore literally means 'many times' or 'varied'.
Es gibt vielfache Gründe für seine Entscheidung.
There are multiple reasons for his decision.
'Vielfach' (often / multiple) can be used as an adverb (unchanged) or as an adjective (declined before a noun). As an adverb, it means 'oft' (often); as an adjective, 'zahlreich' (numerous) or 'vielfältig' (varied).
Er hat sich vielfach für seine Arbeit engagiert.
He has often been involved in his work.
In its adverbial meaning 'oft' (often), 'vielfach' (often) belongs more to written language or a formal style. It is used less often in everyday spoken language.
Wie vielfach berichtet wurde, steigen die Preise weiter an.
As has often been reported, prices continue to rise.
The combination 'auf vielfachen Wunsch' (by popular request / due to multiple requests) is a very common fixed expression. It means that something happens because many people wanted it.
Auf vielfachen Wunsch wird die Ausstellung um einen Monat verlängert.
By popular request, the exhibition will be extended by one month.
often
Oft and vielfach can both express that something happens on many occasions. Vielfach usually sounds more formal and is particularly suitable for factual statements, whereas oft is more common in everyday speech. Use oft in conversation and vielfach mainly in more formal texts.

Vielfach wurde bei dem Treffen über dieses Problem gesprochen.
This problem was discussed many times at the meeting.
Oft wurde bei dem Treffen über dieses Problem gesprochen.
This problem was often discussed at the meeting.