Dogsbody (6)
(Other definitions for drudge that I've seen before include "skivvy" , "Menial servant" , "Person who does dul laborious work" , "One works hard at boring tasks" , "Doer of hard dull work" .)
'dogsbody' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for factotum that I've seen before include "One who does all kinds of work" , "Employee who does all kinds of work (8)" , "Handyman" , "Man Friday" , "Employee with a variety of jobs" .)