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Goodwill and Intangible Assets (Carrying Amount of Goodwill by Reportable Segment) (Details) - USD ($)
$ in Millions
6 Months Ended 12 Months Ended
Jul. 03, 2020
Jan. 03, 2020
Goodwill [Roll Forward]    
Goodwill, Beginning Balance $ 4,912 $ 4,860
Goodwill re-allocation 0 0
Goodwill acquired during period 1,363 50
Divestiture of health staff augmentation business   (5)
Foreign currency translation adjustments (9) 4
Adjustment to goodwill   3
Ending balance, Goodwill 6,266 4,912
Defense Solutions    
Goodwill [Roll Forward]    
Goodwill, Beginning Balance 2,039 2,015
Goodwill re-allocation 429 25
Goodwill acquired during period 764 0
Divestiture of health staff augmentation business   0
Foreign currency translation adjustments (9) (4)
Adjustment to goodwill   3
Ending balance, Goodwill 3,223 2,039
Civil    
Goodwill [Roll Forward]    
Goodwill, Beginning Balance 1,907 1,924
Goodwill re-allocation (429) (25)
Goodwill acquired during period 599 0
Divestiture of health staff augmentation business   0
Foreign currency translation adjustments 0 8
Adjustment to goodwill   0
Ending balance, Goodwill 2,077 1,907
Health    
Goodwill [Roll Forward]    
Goodwill, Beginning Balance 966 921
Goodwill re-allocation 0 0
Goodwill acquired during period 0 50
Divestiture of health staff augmentation business   (5)
Foreign currency translation adjustments 0 0
Adjustment to goodwill   0
Ending balance, Goodwill $ 966 $ 966