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Goodwill and Intangible Assets - Intangible Table by Major Class (Details) - USD ($) $ in Thousands | Nov. 30, 2022 | Aug. 31, 2022
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 3,117,160 | $ 2,971,077
Accumulated Amortization | (1,087,146) | (1,040,269)
Net Carrying Amount | 2,030,014 | 1,930,808
Customer-related |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 2,637,724 | 2,498,001
Accumulated Amortization | (872,216) | (842,056)
Net Carrying Amount | 1,765,508 | 1,655,945
Technology |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 288,708 | 283,251
Accumulated Amortization | (110,107) | (96,782)
Net Carrying Amount | 178,601 | 186,469
Patents |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 126,385 | 126,950
Accumulated Amortization | (70,784) | (70,745)
Net Carrying Amount | 55,601 | 56,205
Other |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 64,343 | 62,875
Accumulated Amortization | (34,039) | (30,686)
Net Carrying Amount | $ 30,304 | $ 32,189

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