4605 ÷ 9 = 511 R6
Alright, let's work through the division of 4605 by 9 step by step.

Step 1:
9 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 9

Step 2:
9 goes into 46 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 45 from 46 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 9

Step 3:
9 goes into 10 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 51
Subtract 9 from 10 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 4:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 511
Subtract 9 from 15 to get 6.

The final result is 511 with a remainder of 6.