51609 ÷ 6 = 8601 R3
Alright, let's work through the division of 51609 by 6 step by step.

Step 1:
6 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 6

Step 2:
6 goes into 51 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 48 from 51 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 3:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 86
Subtract 36 from 36 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 4:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 860
Subtract 0 from 0 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 6

Step 5:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 8601
Subtract 6 from 9 to get 3.

The final result is 8601 with a remainder of 3.