zerlegen
to dismantle
To take an object or machine apart into its individual components.
Der Uhrmacher musste das gesamte Uhrwerk zerlegen, um es zu reinigen.
The watchmaker had to dismantle the entire clockwork mechanism in order to clean it.

to dismantle / analyze
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to dismantle
To take an object or machine apart into its individual components.
Der Uhrmacher musste das gesamte Uhrwerk zerlegen, um es zu reinigen.
The watchmaker had to dismantle the entire clockwork mechanism in order to clean it.

The prefix 'zer-' is inseparable and often emphasizes separation into many small parts, sometimes with a destructive nuance. It indicates that something is being broken down into its components.
Der alte Schrank wurde in seine Einzelteile zerlegt.
The old cabinet was dismantled into its individual parts.
To name the parts into which something is dismantled or broken down, you use the preposition 'in' followed by the accusative. The structure is: [something] in [its parts] zerlegen.
Der Mechaniker zerlegte den Motor in seine Einzelteile.
The mechanic dismantled the engine into its individual parts.
You can recognize the figurative, analytical meaning from the fact that the object of the verb is abstract. In that case, you might analyze a problem, an argument, or a plan, not a physical object.
Lass uns das Problem zerlegen, um eine Lösung zu finden.
Let's break down the problem in order to find a solution.
to share / divide
'teilen' and 'zerlegen' can both mean that something whole becomes smaller parts. 'teilen' is neutral and often simple: you divide paper, cake, or a group into parts. 'zerlegen' sounds more precise when you want to take an object apart into its individual components, for example a device. It can also mean breaking down a problem or a text very precisely into individual points. Learners can confuse the words because in both cases, several parts exist at the end. However, 'zerlegen' is more suitable when you are looking closely at the structure or the individual parts.

In der Werkstatt zerlegt Max den alten Motor in seine Einzelteile.
In the workshop, Max dismantles the old engine into its individual parts.
Die Lehrerin teilt den Text in drei Abschnitte.
The teacher divides the text into three sections.