5638 ÷ 8 = 704 R6
Alright, let's work through the division of 5638 by 8 step by step.

Step 1:
8 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 8

Step 2:
8 goes into 56 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 56 from 56 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 8

Step 3:
8 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 70
Subtract 0 from 3 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 8

Step 4:
8 goes into 38 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 704
Subtract 32 from 38 to get 6.

The final result is 704 with a remainder of 6.