We look at the division of 13171 by 741 
Our goal is to divide 13171 by 741.

Going ahead to step 1:
The number 741 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
Subtract 0 from 1 to get 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 741

Step 2:
When dividing 13 by 741, we get 0 with a remainder of 13.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 13 leaves us with 13.
Grab the next digit (1) from the dividend, add it to 13, then carry on: 131 / 741

Advancing to step 3:
The number 741 fits into 131 0 times, leaving a remainder of 131.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 131 leaves us with 131.
Bring next digit (7) of the dividend behind the 131 and repeat the process: 1317 / 741

Let's proceed to step 4:
The number 741 fits into 1317 1 times, leaving a remainder of 576.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 741 from 1317 and we're left with 576.
Grab the next digit (1) from the dividend, add it to 576, then carry on: 5761 / 741

Let's proceed to step 5:
741 goes into 5761 7 times with a remainder of 574.
Record the quotient 7 as the next digit in the result. 
Result so far: 17.0
Subtracting 5187 from 5761 leaves us with 574.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5740, and continue the process.

On to step 6:
The number 741 fits into 5740 7 times, leaving a remainder of 553.
Record the quotient 7 as the next digit in the result. 
Result so far: 17.7
If we take 5187 away from 5740, we end up with 553.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5530, and continue the process.

Advancing to step 7:
The number 741 fits into 5530 7 times, leaving a remainder of 343.
Put 7 as the next digit of the answer. 
Result so far: 17.77
If we take 5187 away from 5530, we end up with 343.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3430, and continue the process.

In conclusion, the division gives 17.77 with a balance of 0.343.