6781 ÷ 6 = 1130 R1
No problem, we've got 6781 and 6 for the division.

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 (7) of the dividend behind the 0 and repeat the process: 7 / 6

Step 2:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 7 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: 113
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: 1130
Subtract 0 from 1 to get 1.

The final result is 1130 with a remainder of 1.