81779 ÷ 6 = 13629 R5
We're going to perform division on 81779 with 6 as the divisor.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 2:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 21 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 3:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 136
Subtract 36 from 37 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 4:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 1362
Subtract 12 from 17 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 6

Step 5:
6 goes into 59 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 13629
Subtract 54 from 59 to get 5.

The final result is 13629 with a remainder of 5.