We look at the division of 25538 by 59 
We're looking to find how many times 59 goes into 25538.

On to step 1:
59 goes into 2 0 times with a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 59

Step 2:
When dividing 25 by 59, we get 0 with a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 25 leaves us with 25.
Bring next digit (5) of the dividend behind the 25 and repeat the process: 255 / 59

Advancing to step 3:
59 can be fit into 255 4 times, resulting in a remainder of 19.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we subtract 236 from 255, we get 19.
Fetch the next digit (3) from the dividend, attach it to 19 and continue: 193 / 59

Step 4:
59 goes into 193 3 times with a remainder of 16.
The next digit of our result is 3. 
Result so far: 43.0
The remainder is 16 after subtracting 177 from 193.
Take the next digit (8) from the dividend and append it to 16, then repeat: 168 / 59

Advancing to step 5:
The number 59 fits into 168 2 times, leaving a remainder of 50.
The next digit of our result is 2. 
Result so far: 432.0
Subtracting 118 from 168 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 6:
The number 59 fits into 500 8 times, leaving a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 432.8
The remainder is 28 after subtracting 472 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 7:
59 can be fit into 280 4 times, resulting in a remainder of 44.
Record the quotient 4 as the next digit in the result. 
Result so far: 432.84
Subtracting 236 from 280 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 8:
When dividing 440 by 59, we get 7 with a remainder of 27.
The number 7 becomes the next digit in our result. 
Result so far: 432.847
If we take 413 away from 440, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 9:
270 divided by 59 is 4 with a remainder of 34.
Record the quotient 4 as the next digit in the result. 
Result so far: 432.8474
Subtracting 236 from 270 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 10:
340 divided by 59 is 5 with a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 432.84745
Subtracting 295 from 340 leaves us with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 11:
If we divide 450 by 59, we get 7 and a remainder of 37.
The number 7 becomes the next digit in our result. 
Result so far: 432.847457
If we subtract 413 from 450, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 12:
The number 59 fits into 370 6 times, leaving a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 432.8474576
Subtracting 354 from 370 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 13:
The number 59 fits into 160 2 times, leaving a remainder of 42.
Record the quotient 2 as the next digit in the result. 
Result so far: 432.84745762
Subtracting 118 from 160 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

In conclusion, the division gives 432.84745762 with a balance of 4.2e-08.