We're dividing 173641 by 13 
Let's see how many times 13 fits into 173641.

Advancing to step 1:
1 divided by 13 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 13

On to step 2:
If we divide 17 by 13, we get 1 and a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 13 from 17 and we're left with 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 13

Moving on to step 3:
13 can be fit into 43 3 times, resulting in a remainder of 4.
The next digit of our result is 3. 
Result so far: 13.0
If we take 39 away from 43, we end up with 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 13

Going ahead to step 4:
The number 13 fits into 46 3 times, leaving a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 133.0
Deduct 39 from 46 and we're left with 7.
Grab the next digit (4) from the dividend, add it to 7, then carry on: 74 / 13

Moving on to step 5:
13 goes into 74 5 times with a remainder of 9.
The next digit of our result is 5. 
Result so far: 1335.0
Deduct 65 from 74 and we're left with 9.
Fetch the next digit (1) from the dividend, attach it to 9 and continue: 91 / 13

Going ahead to step 6:
The number 13 fits into 91 7 times, leaving a remainder of 0.
The next digit of our result is 7. 
Result so far: 13357.0
Deduct 91 from 91 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 7:
0 divided by 13 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 13357.0
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
13 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 13357.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 13357.0 with a balance of 0.0.