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what part of the computer hardware only retains data while the computer is on
RAM or Volatile storage area is only temporarily memory, requiring electricity to maintain the information stored in it, once the power is off the information is gone.
What part of the computer hardware retains data while the computer is off
A hard disk drive (HDD) is an electro-mechanical data storage device. HDDs are a type of non-volatile storage, retaining stored data even when powered off.

Question: Can I retreive what is deleted
Self-contained rewrite: Can I retreive in the computer the data deleted from the Hard disk