Not living together may become a factor (5)

I believe the answer is:

apart

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'not living together' is the definition.
(I've seen this before)

'a factor' is the wordplay.
'factor' becomes 'part'.
'a'+'part'='APART'

'may become' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for apart that I've seen before include "aloof" , "Asunder" , "Separate in a trap" , "away" , "Unconnected" .)

I've seen this clue in The Telegraph.

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