4508 ÷ 8 = 563 R4
Alright, let's work through the division of 4508 by 8 step by step.

Step 1:
8 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 / 8

Step 2:
8 goes into 45 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 40 from 45 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 8

Step 3:
8 goes into 50 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 56
Subtract 48 from 50 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 8

Step 4:
8 goes into 28 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 563
Subtract 24 from 28 to get 4.

The final result is 563 with a remainder of 4.