Goodwill and Intangible Assets - Intangible Table by Major Class (Details) - USD ($) $ in Thousands	May 31, 2024	Aug. 31, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 4,251,249	$ 3,320,963
Accumulated Amortization	(1,501,284)	(1,248,006)
Net Carrying Amount	2,749,965	2,072,957
Customer-related
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	3,668,580	2,842,257
Accumulated Amortization	(1,216,991)	(999,604)
Net Carrying Amount	2,451,589	1,842,653
Technology
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	328,317	289,989
Accumulated Amortization	(177,196)	(141,022)
Net Carrying Amount	151,121	148,967
Patents
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	121,361	123,579
Accumulated Amortization	(71,860)	(70,472)
Net Carrying Amount	49,501	53,107
Other
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	132,991	65,138
Accumulated Amortization	(35,237)	(36,908)
Net Carrying Amount	$ 97,754	$ 28,230

Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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