Earnings before Income Taxes, Including both Continuing and Discontinued Operations (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2026	Aug. 31, 2025	Aug. 31, 2024
Income Tax Disclosure [Abstract]
Income (Loss) from Continuing Operations before Income Taxes, Domestic	$ 79,300	$ 70,700	$ 59,700
Income (Loss) from Continuing Operations before Income Taxes, Foreign	38,200	50,000	45,800
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest	$ 117,500	$ 120,700	$ 105,500