We're dividing 671727 by 13 
Let's see how many times 13 fits into 671727.

Step 1:
If we divide 6 by 13, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 13

Step 2:
When dividing 67 by 13, we get 5 with a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 65 from 67 and we're left with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 13

Step 3:
21 divided by 13 is 1 with a remainder of 8.
The next digit of our result is 1. 
Result so far: 51.0
The remainder is 8 after subtracting 13 from 21.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 13

On to step 4:
When dividing 87 by 13, we get 6 with a remainder of 9.
The next digit of our result is 6. 
Result so far: 516.0
If we take 78 away from 87, we end up with 9.
Fetch the next digit (2) from the dividend, attach it to 9 and continue: 92 / 13

On to step 5:
The number 13 fits into 92 7 times, leaving a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 5167.0
If we subtract 91 from 92, we get 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 13

Moving on to step 6:
17 divided by 13 is 1 with a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 51671.0
If we take 13 away from 17, 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.

Let's proceed to step 7:
40 divided by 13 is 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 51671.3
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.

Moving on to step 8:
If we divide 10 by 13, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 51671.3
Subtracting 0 from 10 leaves us 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.

Step 9:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 51671.307
If we take 91 away from 100, we end up 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 10:
13 goes into 90 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 51671.3076
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 11:
When dividing 120 by 13, we get 9 with a remainder of 3.
The next digit of our result is 9. 
Result so far: 51671.30769
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.

Let's proceed to step 12:
When dividing 30 by 13, we get 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 51671.307692
Deduct 26 from 30 and we're left 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.

Moving on to step 13:
40 divided by 13 is 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 51671.3076923
If we subtract 39 from 40, we get 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:
13 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 51671.3076923
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.

In conclusion, the division gives 51671.3076923 with a balance of 1e-08.