21597 ÷ 8 = 2699 R5
Alright, let's work through the division of 21597 by 8 step by step.

Step 1:
8 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 8

Step 2:
8 goes into 21 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 16 from 21 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 8

Step 3:
8 goes into 55 6 times with a remainder of 7.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 48 from 55 to get 7.
Bring next digit (9) of the dividend behind the 7 and repeat the process: 79 / 8

Step 4:
8 goes into 79 9 times with a remainder of 7.
Write down 9 as next digit of of the result. 
Result so far: 269
Subtract 72 from 79 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 8

Step 5:
8 goes into 77 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 2699
Subtract 72 from 77 to get 5.

The final result is 2699 with a remainder of 5.