61815 ÷ 6 = 10302 R3
Alright, let's work through the division of 61815 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 (8) of the dividend behind the 1 and repeat the process: 18 / 6

Step 3:
6 goes into 18 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 103
Subtract 18 from 18 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 4:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 1030
Subtract 0 from 1 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: 10302
Subtract 12 from 15 to get 3.

The final result is 10302 with a remainder of 3.