die Gesamtzahl
total number
The sum of all individual elements or quantities; the total amount.
Die Gesamtzahl der Teilnehmer übertraf alle Erwartungen.
The total number of participants exceeded all expectations.

total number
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total number
The sum of all individual elements or quantities; the total amount.
Die Gesamtzahl der Teilnehmer übertraf alle Erwartungen.
The total number of participants exceeded all expectations.

The word is transparently composed of 'gesamt' (whole, total) and 'Zahl' (number). It therefore refers to the sum of all individual numbers.
Bitte berechnen Sie die Gesamtzahl der verkauften Produkte.
Please calculate the total number of products sold.
To express what the total number is made up of, a noun in the genitive usually follows. Alternatively, a 'von' (of/from) construction is also possible.
Die Gesamtzahl der Einwohner ist gestiegen.
The total number of residents has increased.
'Gesamtzahl' (total number) is often combined with verbs that describe a quantity. Typical ones are 'beträgt' (amounts to), 'liegt bei' (stands at), 'steigt' (rises), 'sinkt' (falls), or 'erreicht' (reaches).
Die Gesamtzahl der Bewerbungen liegt bei über 500.
The total number of applications stands at over 500.
number
'die Anzahl' and 'die Gesamtzahl' both mean how many things or people there are. 'Anzahl' can be any counted amount, even just part of a larger group. 'Gesamtzahl' emphasizes that all parts have been added together and that the complete total is meant. If you are only counting a specific group, 'Anzahl' is often enough. If it is important that nothing is missing and everything together is meant, 'Gesamtzahl' fits better.

Bei der Behörde wird morgen die Gesamtzahl der Anträge bekannt gegeben.
The total number of applications will be announced by the government office tomorrow.
Für das Projekt war die Anzahl der Schrauben zu klein.
For the project, the number of screws was too small.