65821 ÷ 8 = 8227 R5
We're going to perform division on 65821 with 8 as the divisor.

Step 1:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 8

Step 2:
8 goes into 65 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 65 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 8

Step 3:
8 goes into 18 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 82
Subtract 16 from 18 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: 822
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: 8227
Subtract 56 from 61 to get 5.

The final result is 8227 with a remainder of 5.