4598 ÷ 9 = 510 R8
Alright, let's work through the division of 4598 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 (5) of the dividend behind the 4 and repeat the process: 45 / 9

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

Step 3:
9 goes into 9 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 51
Subtract 9 from 9 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 9

Step 4:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of of the result. 
Result so far: 510
Subtract 0 from 8 to get 8.

The final result is 510 with a remainder of 8.