We're dividing 76681 by 6 
We're looking to find how many times 6 goes into 76681.

Going ahead to step 1:
When dividing 7 by 6, we get 1 with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 6 from 7 to get 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 6

Moving on to step 2:
If we divide 16 by 6, we get 2 and a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Deduct 12 from 16 and we're left with 4.
Grab the next digit (6) from the dividend, add it to 4, then carry on: 46 / 6

Going ahead to step 3:
6 can be fit into 46 7 times, resulting in a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 127.0
If we subtract 42 from 46, we get 4.
Append the next digit (8) from the dividend to 4 and continue with: 48 / 6

Going ahead to step 4:
48 divided by 6 is 8 with a remainder of 0.
Use 8 as the next digit of our solution. 
Result so far: 1278.0
The remainder is 0 after subtracting 48 from 48.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 6

On to step 5:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 12780.0
If we take 0 away from 1, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 6:
6 can be fit into 10 1 times, resulting in a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 12780.1
Subtract 6 from 10 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 7:
If we divide 40 by 6, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 12780.16
If we subtract 36 from 40, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 8:
When dividing 40 by 6, we get 6 with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 12780.166
Subtract 36 from 40 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final result is 12780.166 with a remainder of 0.0004.