1. Peel the potatoes and cut them in pieces.

2. Peel the potatoes and cut them into pieces.
3. Peel the potatoes and cut them in three pieces.
4. Peel the potatoes and cut them into three pieces.
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Are they all grammatical? Do we have to use 'in' or 'into'?
Are both okay? Which ones are commonly used?

We use both. I prefer "into", but people say it with both "in" and "into".