57666 ÷ 9 = 6407 R3
Alright, let's work through the division of 57666 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 (6) of the dividend behind the 3 and repeat the process: 36 / 9

Step 3:
9 goes into 36 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 64
Subtract 36 from 36 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 9

Step 4:
9 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 640
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

Step 5:
9 goes into 66 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 6407
Subtract 63 from 66 to get 3.

The final result is 6407 with a remainder of 3.