57743 ÷ 9 = 6415 R8
Alright, let's work through the division of 57743 by 9 step by step.

Step 1:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 9

Step 2:
9 goes into 57 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 54 from 57 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 3:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 64
Subtract 36 from 37 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 9

Step 4:
9 goes into 14 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 641
Subtract 9 from 14 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 9

Step 5:
9 goes into 53 5 times with a remainder of 8.
Write down 5 as next digit of of the result. 
Result so far: 6415
Subtract 45 from 53 to get 8.

The final result is 6415 with a remainder of 8.