82201 ÷ 8 = 10275 R1
Alright, let's work through the division of 82201 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 (2) of the dividend behind the 0 and repeat the process: 2 / 8

Step 2:
8 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 2 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 8

Step 3:
8 goes into 22 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 16 from 22 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 8

Step 4:
8 goes into 60 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 1027
Subtract 56 from 60 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 8

Step 5:
8 goes into 41 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 10275
Subtract 40 from 41 to get 1.

The final result is 10275 with a remainder of 1.