23221 ÷ 6 = 3870 R1
Alright, let's work through the division of 23221 by 6 step by step.

Step 1:
6 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 (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 2:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 18 from 23 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 6

Step 3:
6 goes into 52 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 38
Subtract 48 from 52 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 6

Step 4:
6 goes into 42 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 387
Subtract 42 from 42 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 5:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 3870
Subtract 0 from 1 to get 1.

The final result is 3870 with a remainder of 1.