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Earnings Per Common Share (Tables)
6 Months Ended
Jun. 30, 2021
Earnings Per Share [Abstract]  
Schedule of computation of basic and diluted earnings per common share
The following table sets forth the computation of basic and diluted earnings per common share:
Three Months EndedSix Months Ended
June 30,June 30,
 2021202020212020
Numerator:
Net income (loss)$718,664 $466,389 $1,194,372 $377,715 
Amounts attributable to noncontrolling interests(43,178)(167,568)(80,730)65,223 
Net income (loss) available to Arch675,486 298,821 1,113,642 442,938 
Preferred dividends(11,666)(10,403)(22,069)(20,806)
Net income (loss) available to Arch common shareholders$663,820 $288,418 $1,091,573 $422,132 
Denominator:
Weighted average common shares and common share equivalents outstanding — basic397,743,402 402,503,687 399,267,183 403,197,924 
Effect of dilutive common share equivalents:
Nonvested restricted shares1,990,729 1,597,701 1,932,929 1,829,239 
Stock options (1)6,751,863 4,018,293 6,487,568 5,978,428 
Weighted average common shares and common share equivalents outstanding — diluted406,485,994 408,119,681 407,687,680 411,005,591 
Earnings per common share:
Basic$1.67 $0.72 $2.73 $1.05 
Diluted$1.63 $0.71 $2.68 $1.03 
(1)    Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For the 2021 second quarter and 2020 second quarter, the number of stock options excluded were 1,974,849 and 6,982,107, respectively. For the six months ended June 30, 2021 and 2020 period, the number of stock options excluded were 2,395,749 and 2,038,758, respectively.