99321 ÷ 6 = 16553 R3
Alright, let's work through the division of 99321 by 6 step by step.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 6

Step 2:
6 goes into 39 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 36 from 39 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 3:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 165
Subtract 30 from 33 to get 3.
Bring next digit (2) of the dividend behind the 3 and repeat the process: 32 / 6

Step 4:
6 goes into 32 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 1655
Subtract 30 from 32 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 5:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 16553
Subtract 18 from 21 to get 3.

The final result is 16553 with a remainder of 3.