65559 ÷ 6 = 10926 R3
Alright, let's work through the division of 65559 by 6 step by step.

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 (5) of the dividend behind the 5 and repeat the process: 55 / 6

Step 3:
6 goes into 55 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 109
Subtract 54 from 55 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 4:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 1092
Subtract 12 from 15 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 6

Step 5:
6 goes into 39 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 10926
Subtract 36 from 39 to get 3.

The final result is 10926 with a remainder of 3.