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Summary of Significant Accounting Policies - Additional Information (Detail)
$ / shares in Units, $ in Thousands
 12 Months Ended
Jan. 02, 2024
USD ($)
Sep. 08, 2023
USD ($)
Apr. 24, 2023
USD ($)
Oct. 27, 2022
USD ($)
Mar. 12, 2021
USD ($)
Dec. 31, 2023
USD ($)
segment
$ / shares
Dec. 31, 2022
USD ($)
$ / shares
Dec. 31, 2021
USD ($)
$ / shares
Sep. 30, 2023
Jun. 30, 2023
Significant Accounting Policies [Line Items]                    
Number of operating segments | segment           2        
Depreciation           $ (126,000) $ (109,800) $ (92,100)    
Fixed-income securities investment portfolio, maximum effective maturity           40 months        
Foreign currency net gains (losses)           $ (7,000) (43,800) (13,300)    
Accounts receivable sold under factoring arrangements           51,200 37,000      
Costs to obtain contracts           25,100 27,400      
Amortization of costs to obtain contracts           12,500 20,800 17,000    
Revenue remaining performance obligation           1,578,300 1,515,400      
Amount awarded   $ 63,000   $ 63,000 $ 43,400          
Settlement gain           0 0 43,403    
Advertising cost           201,200 222,000 325,600    
Purchase of equity investment           76,999 0 0    
Net income           $ 445,053 $ 361,573 $ 772,020    
Basic (usd per share) | $ / shares           $ 5.82 $ 4.62 $ 9.78    
Diluted (usd per share) | $ / shares           $ 5.81 $ 4.61 $ 9.69    
Cubicure | Subsequent Event                    
Significant Accounting Policies [Line Items]                    
Purchase price $ 87,000                  
Heartland                    
Significant Accounting Policies [Line Items]                    
Equity interest     5.00%              
Purchase of equity investment     $ 75,000              
Investments in equity securities           $ 75,000        
Service Life                    
Significant Accounting Policies [Line Items]                    
Depreciation           5,400        
Net income           $ 3,700        
Basic (usd per share) | $ / shares           $ 0.05        
Diluted (usd per share) | $ / shares           $ 0.05        
Service Life | Clinical and manufacturing equipment                    
Significant Accounting Policies [Line Items]                    
Estimated useful life                 13 years 10 years
Clear Aligner                    
Significant Accounting Policies [Line Items]                    
Warranty period           3 months        
Intraoral Scanners                    
Significant Accounting Policies [Line Items]                    
Warranty period           1 year        
CAD/CAM Software                    
Significant Accounting Policies [Line Items]                    
Warranty period           1 year        
Invisalign | Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2024-01-01                    
Significant Accounting Policies [Line Items]                    
Expected timing           6 months        
Invisalign | Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2024-07-01                    
Significant Accounting Policies [Line Items]                    
Expected timing           5 years        
Systems and Services | Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2024-01-01                    
Significant Accounting Policies [Line Items]                    
Expected timing           1 year        
Systems and Services | Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2025-01-01                    
Significant Accounting Policies [Line Items]                    
Expected timing           5 years        
Minimum                    
Significant Accounting Policies [Line Items]                    
Estimated useful lives of intangibles           8 years        
Maximum                    
Significant Accounting Policies [Line Items]                    
Estimated useful lives of intangibles           10 years        
Maximum | Clinical and manufacturing equipment                    
Significant Accounting Policies [Line Items]                    
Estimated useful life           13 years