We're dividing 172603 by 25 
We're looking to find how many times 25 goes into 172603.

Advancing to step 1:
25 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 25

On to step 2:
17 divided by 25 is 0 with a remainder of 17.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Bring next digit (2) of the dividend behind the 17 and repeat the process: 172 / 25

Let's proceed to step 3:
172 divided by 25 is 6 with a remainder of 22.
The next digit of our result is 6. 
Result so far: 6.0
If we subtract 150 from 172, we get 22.
Bring next digit (6) of the dividend behind the 22 and repeat the process: 226 / 25

Going ahead to step 4:
If we divide 226 by 25, we get 9 and a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 69.0
The remainder is 1 after subtracting 225 from 226.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 25

Let's proceed to step 5:
10 divided by 25 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 690.0
If we subtract 0 from 10, we get 10.
Append the next digit (3) from the dividend to 10 and continue with: 103 / 25

Advancing to step 6:
The number 25 fits into 103 4 times, leaving a remainder of 3.
The next digit of our result is 4. 
Result so far: 6904.0
Deduct 100 from 103 and we're left 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.

Moving on to step 7:
30 divided by 25 is 1 with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 6904.1
Subtract 25 from 30 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 8:
If we divide 50 by 25, we get 2 and a remainder of 0.
The next digit of our result is 2. 
Result so far: 6904.12
Deduct 50 from 50 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.

Advancing to step 9:
25 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 6904.12
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.

Going ahead to step 10:
25 can be fit into 0 0 times, resulting in a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 6904.12
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 6904.12 with a balance of 0.0.