66349 ÷ 9 = 7372 R1
Alright, let's work through the division of 66349 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 (3) of the dividend behind the 3 and repeat the process: 33 / 9

Step 3:
9 goes into 33 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 73
Subtract 27 from 33 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 9

Step 4:
9 goes into 64 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 737
Subtract 63 from 64 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 9

Step 5:
9 goes into 19 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 7372
Subtract 18 from 19 to get 1.

The final result is 7372 with a remainder of 1.