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Goodwill and Intangible Assets - Intangible Table by Major Class (Details) - USD ($) $ in Thousands | May 31, 2025 | Aug. 31, 2024
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 4,469,312 | $ 4,530,739
Accumulated Amortization | (1,877,627) | (1,626,708)
Net Carrying Amount | 2,591,685 | 2,904,031
Customer-related |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 3,884,301 | 3,924,339
Accumulated Amortization | (1,549,918) | (1,336,679)
Net Carrying Amount | 2,334,383 | 2,587,660
Technology |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 347,369 | 335,845
Accumulated Amortization | (220,185) | (183,182)
Net Carrying Amount | 127,184 | 152,663
Patents |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 115,644 | 120,457
Accumulated Amortization | (72,757) | (72,518)
Net Carrying Amount | 42,887 | 47,939
Other |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 121,998 | 150,098
Accumulated Amortization | (34,767) | (34,329)
Net Carrying Amount | $ 87,231 | $ 115,769

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