65606 ÷ 6 = 10934 R2
Let's divide 65606 by 6.

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

Step 2:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 5 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 3:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 109
Subtract 54 from 56 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 6

Step 4:
6 goes into 20 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 1093
Subtract 18 from 20 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 6

Step 5:
6 goes into 26 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 10934
Subtract 24 from 26 to get 2.

The final result is 10934 with a remainder of 2.