Revenue from Contracts with Customers - Schedule of Disaggregation of Revenue (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 01, 2022	Oct. 02, 2021	Oct. 03, 2020
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	$ 3,927,643	$ 3,480,676	$ 3,501,782
Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	3,811,368	3,368,865	3,390,394
Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	116,275	111,811	111,388
Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,752,718	1,548,975	1,520,441
Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,565,771	1,326,772	1,258,385
Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	492,879	493,118	611,568
AMER
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,310,688	1,317,404	1,327,849
AMER | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,300,403	1,307,352	1,317,120
AMER | Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	10,285	10,052	10,729
AMER | Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	398,743	462,789	481,301
AMER | Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	645,881	566,693	464,134
AMER | Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	255,779	277,870	371,685
APAC
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	2,300,640	1,850,603	1,824,831
APAC | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	2,198,225	1,750,924	1,730,476
APAC | Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	102,415	99,679	94,355
APAC | Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,288,577	1,010,833	954,925
APAC | Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	744,216	605,249	618,250
APAC | Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	165,432	134,842	157,301
EMEA
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	316,315	312,669	349,102
EMEA | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	312,740	310,589	342,798
EMEA | Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	3,575	2,080	6,304
EMEA | Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	65,398	75,353	84,215
EMEA | Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	175,674	154,830	176,001
EMEA | Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	$ 71,668	$ 80,406	$ 82,582