687112 ÷ 13 
Let's see how many times 13 fits into 687112.

Advancing to step 1:
6 divided by 13 is 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 13

On to step 2:
13 goes into 68 5 times with a remainder of 3.
The next digit of our result is 5. 
Result so far: 5.0
Subtracting 65 from 68 leaves us with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 13

On to step 3:
When dividing 37 by 13, we get 2 with a remainder of 11.
Use 2 as the next digit of our solution. 
Result so far: 52.0
The remainder is 11 after subtracting 26 from 37.
Include the next digit (1) from the dividend after 11, then repeat: 111 / 13

Let's proceed to step 4:
13 can be fit into 111 8 times, resulting in a remainder of 7.
The next digit of our result is 8. 
Result so far: 528.0
If we subtract 104 from 111, we get 7.
Append the next digit (1) from the dividend to 7 and continue with: 71 / 13

Step 5:
13 can be fit into 71 5 times, resulting in a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 5285.0
If we take 65 away from 71, we end up with 6.
Bring next digit (2) of the dividend behind the 6 and repeat the process: 62 / 13

Advancing to step 6:
If we divide 62 by 13, we get 4 and a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 52854.0
The remainder is 10 after subtracting 52 from 62.
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 7:
13 goes into 100 7 times with a remainder of 9.
The next digit of our result is 7. 
Result so far: 52854.7
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 52854.76
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 9:
120 divided by 13 is 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 52854.769
Subtract 117 from 120 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 10:
30 divided by 13 is 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 52854.7692
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 11:
When dividing 40 by 13, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 52854.76923
If we take 39 away from 40, 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 12:
13 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: 52854.76923
If we subtract 0 from 10, we 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.

Let's proceed to step 13:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 52854.7692307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 14:
90 divided by 13 is 6 with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 52854.76923076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 52854.76923076 with a balance of 1.2e-08.