We're dividing 687288 by 13 
We're looking to find how many times 13 goes into 687288.

Step 1:
When dividing 6 by 13, we get 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 13

Going ahead to step 2:
68 divided by 13 is 5 with a remainder of 3.
The next digit of our result is 5. 
Result so far: 5.0
Deduct 65 from 68 and we're left with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 13

On to step 3:
13 can be fit into 37 2 times, resulting in a remainder of 11.
The next digit of our result is 2. 
Result so far: 52.0
If we subtract 26 from 37, we get 11.
Grab the next digit (2) from the dividend, add it to 11, then carry on: 112 / 13

Step 4:
The number 13 fits into 112 8 times, leaving a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 528.0
If we take 104 away from 112, we end up with 8.
Append the next digit (8) from the dividend to 8 and continue with: 88 / 13

Going ahead to step 5:
When dividing 88 by 13, we get 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 5286.0
If we take 78 away from 88, we end up with 10.
Bring next digit (8) of the dividend behind the 10 and repeat the process: 108 / 13

Let's proceed to step 6:
If we divide 108 by 13, we get 8 and a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 52868.0
If we subtract 104 from 108, 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.

Moving on to step 7:
If we divide 40 by 13, we get 3 and a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 52868.3
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.

On to step 8:
13 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 52868.3
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.

Going ahead to step 9:
The number 13 fits into 100 7 times, leaving a remainder of 9.
The next digit of our result is 7. 
Result so far: 52868.307
Subtract 91 from 100 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 10:
90 divided by 13 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 52868.3076
Subtracting 78 from 90 leaves us 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.

Advancing to step 11:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 52868.30769
If we subtract 117 from 120, we 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.

Step 12:
If we divide 30 by 13, we get 2 and a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 52868.307692
Subtracting 26 from 30 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 13:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 52868.3076923
Subtracting 39 from 40 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.

Going ahead to step 14:
10 divided by 13 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 52868.3076923
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 52868.3076923 with a balance of 1e-08.