10681 ÷ 15 
Let's see how many times 15 fits into 10681.

Let's proceed to step 1:
15 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 15

On to step 2:
15 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 15

Step 3:
106 divided by 15 is 7 with a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtracting 105 from 106 leaves us with 1.
Fetch the next digit (8) from the dividend, attach it to 1 and continue: 18 / 15

Let's proceed to step 4:
15 goes into 18 1 times with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 71.0
If we take 15 away from 18, we end up with 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 15

Advancing to step 5:
If we divide 31 by 15, we get 2 and a remainder of 1.
The next digit of our result is 2. 
Result so far: 712.0
Subtracting 30 from 31 leaves us 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.

Let's proceed to step 6:
15 can be fit into 10 0 times, resulting in a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 712.0
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 7:
The number 15 fits into 100 6 times, leaving a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 712.06
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
100 divided by 15 is 6 with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 712.066
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 712.066, and the remainder is 0.001.