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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, 2024
Aug. 31, 2023
Aug. 31, 2022
Earnings per share      
Net income $ 422.6 $ 346.0 $ 384.0
Basic weighted average shares outstanding (in shares) [1] 30,885 31,806 34,182
Common stock equivalents (in shares) 560 358 463
Diluted weighted average number of shares outstanding (in shares) [1] 31,445 32,164 34,645
Basic earnings per share (in dollars per share) [1] $ 13.68 $ 10.88 $ 11.23
Diluted earnings per share (in dollars per share) [1] $ 13.44 $ 10.76 $ 11.08
Stock options      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 100 100
Restricted stock awards and units      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 100 100
Performance stock units      
Earnings per share      
Stock options (less than) excluded from diluted earnings per share (in shares) 100 100 0
[1] Earnings per share is calculated using unrounded numbers. Amounts in the table may not recalculate exactly due to rounding.