61779 ÷ 6 = 10296 R3
Alright, let's work through the division of 61779 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 (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 3:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 12 from 17 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 4:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 1029
Subtract 54 from 57 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: 10296
Subtract 36 from 39 to get 3.

The final result is 10296 with a remainder of 3.