10511906 ÷ 686 
We're looking to find how many times 686 goes into 10511906.

Step 1:
The number 686 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 686

Let's proceed to step 2:
686 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
If we subtract 0 from 10, we get 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 686

On to step 3:
686 can be fit into 105 0 times, resulting in a remainder of 105.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 105 after subtracting 0 from 105.
Include the next digit (1) from the dividend after 105, then repeat: 1051 / 686

On to step 4:
686 goes into 1051 1 times with a remainder of 365.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 686 from 1051 and we're left with 365.
Include the next digit (1) from the dividend after 365, then repeat: 3651 / 686

On to step 5:
The number 686 fits into 3651 5 times, leaving a remainder of 221.
Put 5 as the next digit of the answer. 
Result so far: 15.0
If we take 3430 away from 3651, we end up with 221.
Fetch the next digit (9) from the dividend, attach it to 221 and continue: 2219 / 686

Moving on to step 6:
When dividing 2219 by 686, we get 3 with a remainder of 161.
Record the quotient 3 as the next digit in the result. 
Result so far: 153.0
Subtracting 2058 from 2219 leaves us with 161.
Grab the next digit (0) from the dividend, add it to 161, then carry on: 1610 / 686

Let's proceed to step 7:
686 can be fit into 1610 2 times, resulting in a remainder of 238.
Use 2 as the next digit of our solution. 
Result so far: 1532.0
The remainder is 238 after subtracting 1372 from 1610.
Append the next digit (6) from the dividend to 238 and continue with: 2386 / 686

On to step 8:
When dividing 2386 by 686, we get 3 with a remainder of 328.
Use 3 as the next digit of our solution. 
Result so far: 15323.0
Subtract 2058 from 2386 to get 328.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3280, and continue the process.

Advancing to step 9:
3280 divided by 686 is 4 with a remainder of 536.
The number 4 becomes the next digit in our result. 
Result so far: 15323.4
Subtracting 2744 from 3280 leaves us with 536.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5360, and continue the process.

Advancing to step 10:
When dividing 5360 by 686, we get 7 with a remainder of 558.
Record the quotient 7 as the next digit in the result. 
Result so far: 15323.47
Deduct 4802 from 5360 and we're left with 558.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5580, and continue the process.

Moving on to step 11:
686 can be fit into 5580 8 times, resulting in a remainder of 92.
Record the quotient 8 as the next digit in the result. 
Result so far: 15323.478
Subtract 5488 from 5580 to get 92.
Since there are no more digits in the dividend, we add a zero to the remainder making it 920, and continue the process.

Step 12:
The number 686 fits into 920 1 times, leaving a remainder of 234.
Record the quotient 1 as the next digit in the result. 
Result so far: 15323.4781
Subtract 686 from 920 to get 234.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2340, and continue the process.

Advancing to step 13:
686 can be fit into 2340 3 times, resulting in a remainder of 282.
The number 3 becomes the next digit in our result. 
Result so far: 15323.47813
Deduct 2058 from 2340 and we're left with 282.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2820, and continue the process.

Going ahead to step 14:
The number 686 fits into 2820 4 times, leaving a remainder of 76.
Write down 4 as next digit of the result. 
Result so far: 15323.478134
Subtract 2744 from 2820 to get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Going ahead to step 15:
The number 686 fits into 760 1 times, leaving a remainder of 74.
Record the quotient 1 as the next digit in the result. 
Result so far: 15323.4781341
The remainder is 74 after subtracting 686 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Let's proceed to step 16:
If we divide 740 by 686, we get 1 and a remainder of 54.
Use 1 as the next digit of our solution. 
Result so far: 15323.47813411
If we subtract 686 from 740, we get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

In conclusion, the division gives 15323.47813411 with a balance of 5.4e-08.