9783 ÷ 6 = 1630 R3
Alright, let's work through the division of 9783 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 (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 2:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 36 from 37 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 6

Step 3:
6 goes into 18 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 163
Subtract 18 from 18 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 4:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 1630
Subtract 0 from 3 to get 3.

The final result is 1630 with a remainder of 3.