84221 ÷ 8 = 10527 R5
Alright, let's work through the division of 84221 by 8 step by step.

Step 1:
8 goes into 8 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 8 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 8

Step 2:
8 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 4 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 8

Step 3:
8 goes into 42 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 105
Subtract 40 from 42 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 8

Step 4:
8 goes into 22 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 1052
Subtract 16 from 22 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 8

Step 5:
8 goes into 61 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 10527
Subtract 56 from 61 to get 5.

The final result is 10527 with a remainder of 5.