We're dividing 687041 by 13 
We're looking to find how many times 13 goes into 687041.

Going ahead to step 1:
The number 13 fits into 6 0 times, leaving a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 13

Advancing to step 2:
If we divide 68 by 13, we get 5 and 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.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 13

Moving on to step 3:
13 can be fit into 37 2 times, resulting in a remainder of 11.
Record the quotient 2 as the next digit in the result. 
Result so far: 52.0
Deduct 26 from 37 and we're left with 11.
Take the next digit (0) from the dividend and append it to 11, then repeat: 110 / 13

Step 4:
110 divided by 13 is 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 528.0
Subtract 104 from 110 to get 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 13

Moving on to step 5:
13 goes into 64 4 times with a remainder of 12.
The next digit of our result is 4. 
Result so far: 5284.0
Deduct 52 from 64 and we're left with 12.
Include the next digit (1) from the dividend after 12, then repeat: 121 / 13

Moving on to step 6:
If we divide 121 by 13, we get 9 and a remainder of 4.
The next digit of our result is 9. 
Result so far: 52849.0
If we subtract 117 from 121, 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:
13 goes into 40 3 times with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 52849.3
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.

Let's proceed to step 8:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 52849.3
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.

Moving on to step 9:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 52849.307
Deduct 91 from 100 and we're left 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.

Moving on to step 10:
13 goes into 90 6 times with a remainder of 12.
The next digit of our result is 6. 
Result so far: 52849.3076
Deduct 78 from 90 and we're left 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.

Step 11:
When dividing 120 by 13, we get 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 52849.30769
Subtracting 117 from 120 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 12:
If we divide 30 by 13, we get 2 and a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 52849.307692
If we take 26 away from 30, we end up 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.

On to step 13:
13 goes into 40 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 52849.3076923
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.

Step 14:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 52849.3076923
If we take 0 away from 10, we end up 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.

Our division results in 52849.3076923 with a remaining 1e-08.