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Common Stock and Related Matters - Earnings per Share (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
 12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Earnings per share      
Net income $ 384.0 $ 306.3 $ 248.3
Basic weighted average shares outstanding (in shares) 34,182 36,284 39,453
Common stock equivalents (in shares) 463 270 148
Diluted weighted average number of shares outstanding (in shares) 34,645 36,554 39,601
Basic earnings per share (in dollars per share) [1] $ 11.23 $ 8.44 $ 6.29
Diluted earnings per share (in dollars per share) [1] $ 11.08 $ 8.38 $ 6.27
Stock options      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 800 600
Restricted stock awards and units      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 100 200
Performance stock units      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 0 0 100
[1] (1) Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.