61017 ÷ 6 = 10169 R3
Alright, let's work through the division of 61017 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 (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 2:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 3:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 101
Subtract 6 from 10 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 4:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 1016
Subtract 36 from 41 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 5:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 10169
Subtract 54 from 57 to get 3.

The final result is 10169 with a remainder of 3.