13629 ÷ 25 
We're looking to find how many times 25 goes into 13629.

Let's proceed to step 1:
If we divide 1 by 25, we get 0 and 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 / 25

Going ahead to step 2:
When dividing 13 by 25, we get 0 with a remainder of 13.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 13, we end up with 13.
Grab the next digit (6) from the dividend, add it to 13, then carry on: 136 / 25

On to step 3:
136 divided by 25 is 5 with a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 5.0
The remainder is 11 after subtracting 125 from 136.
Bring next digit (2) of the dividend behind the 11 and repeat the process: 112 / 25

Going ahead to step 4:
The number 25 fits into 112 4 times, leaving a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 54.0
Subtract 100 from 112 to get 12.
Bring next digit (9) of the dividend behind the 12 and repeat the process: 129 / 25

Moving on to step 5:
25 can be fit into 129 5 times, resulting in a remainder of 4.
Write down 5 as next digit of the result. 
Result so far: 545.0
Subtract 125 from 129 to 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.

Step 6:
40 divided by 25 is 1 with a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 545.1
If we subtract 25 from 40, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 7:
If we divide 150 by 25, we get 6 and a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 545.16
If we take 150 away from 150, we end up 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.

On to step 8:
0 divided by 25 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 545.16
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.

On to step 9:
0 divided by 25 is 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 545.16
If we take 0 away from 0, we end up 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.

In conclusion, the division gives 545.16 with a balance of 0.0.