10935 ÷ 6 = 1822 R3
Alright, let's work through the division of 10935 by 6 step by step.

Step 1:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 2:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 10 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 6

Step 3:
6 goes into 49 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 18
Subtract 48 from 49 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 6

Step 4:
6 goes into 13 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 182
Subtract 12 from 13 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 5:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1822
Subtract 12 from 15 to get 3.

The final result is 1822 with a remainder of 3.