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Common Stock and Related Matters - Earnings per Share (Details) - USD ($)
$ / shares in Units, $ in Millions
 12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Earnings per share:      
Net income $ 306.3 $ 248.3 $ 330.4
Basic weighted average shares outstanding (in shares) 36,300,000 39,500,000 39,700,000
Common stock equivalents (in shares) 300,000 100,000 100,000
Diluted weighted average number of shares outstanding (in shares) 36,600,000 39,600,000 39,800,000
Basic earnings per share (in dollars per share) $ 8.44 $ 6.29 $ 8.32
Diluted earnings per share (in dollars per share) $ 8.38 $ 6.27 $ 8.29
Stock options      
Earnings per share:      
Stock options excluded from diluted earnings per share (in shares) 800,000 600,000 300,000
Restricted stock awards and units      
Earnings per share:      
Stock options excluded from diluted earnings per share (in shares) 0 200,000 200,000
Performance stock units      
Earnings per share:      
Stock options excluded from diluted earnings per share (in shares) 0 0 0