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Share-based Payments - Estimate Fair Value of Stock Options (Details) - Stock options - Stock Incentive Plan - $ / shares
12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Market Options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Dividend yield 0.50% 0.40%  
Expected volatility 36.50% 33.70%  
Risk-free interest rate 0.70% 1.50%  
Expected life of options 8 years 7 years  
Weighted-average fair value of options (in dollars per share) $ 40.45 $ 44.74  
Service Options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Dividend yield   0.40% 0.40%
Expected volatility   33.70% 32.80%
Risk-free interest rate   1.30% 3.00%
Expected life of options   5 years 4 years
Weighted-average fair value of options (in dollars per share)   $ 34.22 $ 34.06