66126 ÷ 9 = 7347 R3
Alright, let's work through the division of 66126 by 9 step by step.

Step 1:
9 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

Step 2:
9 goes into 66 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 63 from 66 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 9

Step 3:
9 goes into 31 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 73
Subtract 27 from 31 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 9

Step 4:
9 goes into 42 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 734
Subtract 36 from 42 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: 7347
Subtract 63 from 66 to get 3.

The final result is 7347 with a remainder of 3.