Unaudited Quarterly Financial Data (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended								12 Months Ended
	Aug. 31, 2020	May 31, 2020	Feb. 28, 2020	Nov. 30, 2019	Aug. 31, 2019	May 31, 2019	Feb. 28, 2019	Nov. 30, 2018	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018
Quarterly Financial Information Disclosure [Abstract]
Revenue	$ 383,590	$ 374,083	$ 369,780	$ 366,658	$ 364,283	$ 364,533	$ 354,895	$ 351,640	$ 1,494,111	$ 1,435,351	$ 1,350,145
Cost of services	183,568	170,703	176,218	164,957	167,730	163,832	165,108	166,776	695,446	663,446	659,296
Selling, general and administrative	101,445	81,740	87,305	88,515	84,985	83,461	81,099	84,325	359,005	333,870	324,645
Operating income	98,577	121,640	106,257	113,186	111,568	117,240	108,688	100,539	439,660	438,035	366,204
Net income	$ 89,079	$ 101,216	$ 88,686	$ 93,957	$ 91,527	$ 92,265	$ 84,702	$ 84,296	$ 372,938	$ 352,790	$ 267,085
Diluted EPS (in dollars per share)	$ 2.29	$ 2.63	$ 2.30	$ 2.43	$ 2.34	$ 2.37	$ 2.19	$ 2.17	$ 9.65	$ 9.08	$ 6.78
Diluted weighted average common shares (in shares)	38,940	38,481	38,576	38,587	39,056	38,993	38,619	38,809	38,646	38,873	39,377