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Stock-based Compensation (Narrative) (Details) - USD ($)	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Number of shares authorized under stock plan	1,000,000
Number of shares available for grant	172,878
Employee service share-based, Tax benefit from compensation expense	$ 1,300,000	$ 1,500,000	$ 2,000,000
Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)	23,732
Employee service share-based, Tax benefit from compensation expense	$ 800,000	$ 600,000	$ 1,900,000
Compensation cost not yet recognized	$ 1,000,000
Remaining weighted-average vesting periods	1 year 9 months 18 days
Weighted-average grant date fair value (in dollars per share)	$ 167.05	$ 217.03	$ 208.29
Intrinsic value of shares converted	$ 3,700,000	$ 3,000,000	$ 8,500,000
Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)	13,695
Employee service share-based, Tax benefit from compensation expense		$ 900,000	$ 1,300,000
Compensation cost not yet recognized	$ 2,400,000
Remaining weighted-average vesting periods	1 year 10 months 17 days
Weighted-average grant date fair value (in dollars per share)	$ 184.15	$ 232.99	$ 184.96
Intrinsic value of shares converted	$ 0	$ 4,400,000	$ 5,900,000
Expected volatility period	2 years 10 months 20 days	2 years 10 months 20 days	2 years 10 months 17 days
Deferred Performance Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Granted (in shares)			0
Compensation cost not yet recognized	$ 0
Performance Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Period of separation from service			6 months
Granted (in shares)	21,990
Employee service share-based, Tax benefit from compensation expense		$ 800,000	$ 0
Compensation cost not yet recognized	$ 0
Weighted-average grant date fair value (in dollars per share)	$ 170.16	$ 227.24	$ 197.51
Intrinsic value of shares converted	$ 0	$ 4,000,000
Vesting percentage			100.00%
Key Executives \| Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting period	3 years
Period of separation from service	6 months
High Level Employees \| Restricted Stock Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting period	3 years
High Level Employees \| Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting period	3 years
Minimum \| Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	0.00%
Minimum \| Performance Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	0.00%
Maximum \| Market Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	200.00%
Maximum \| Performance Share Units
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Vesting percentage	100.00%