681953 divided by 6 
We're looking to find how many times 6 goes into 681953.

Going ahead to step 1:
If we divide 6 by 6, we get 1 and a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 6 from 6 leaves us with 0.
Append the next digit (8) from the dividend to 0 and continue with: 8 / 6

On to step 2:
6 can be fit into 8 1 times, resulting in a remainder of 2.
The next digit of our result is 1. 
Result so far: 11.0
Deduct 6 from 8 and we're left with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 6

Step 3:
6 goes into 21 3 times with a remainder of 3.
The next digit of our result is 3. 
Result so far: 113.0
If we take 18 away from 21, we end up with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 6

Let's proceed to step 4:
6 can be fit into 39 6 times, resulting in a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 1136.0
The remainder is 3 after subtracting 36 from 39.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 6

Moving on to step 5:
When dividing 35 by 6, we get 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 11365.0
If we subtract 30 from 35, we get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 6

Let's proceed to step 6:
6 goes into 53 8 times with a remainder of 5.
The next digit of our result is 8. 
Result so far: 113658.0
Subtract 48 from 53 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
6 can be fit into 50 8 times, resulting in a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 113658.8
The remainder is 2 after subtracting 48 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
6 goes into 20 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 113658.83
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 9:
If we divide 20 by 6, we get 3 and a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 113658.833
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 113658.833, and the remainder is 0.0002.