We look at the division of 41578 by 25 
We're looking to find how many times 25 goes into 41578.

Step 1:
When dividing 4 by 25, we get 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 25

Moving on to step 2:
When dividing 41 by 25, we get 1 with a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 16 after subtracting 25 from 41.
Append the next digit (5) from the dividend to 16 and continue with: 165 / 25

Going ahead to step 3:
25 goes into 165 6 times with a remainder of 15.
The number 6 becomes the next digit in our result. 
Result so far: 16.0
If we take 150 away from 165, we end up with 15.
Append the next digit (7) from the dividend to 15 and continue with: 157 / 25

Let's proceed to step 4:
157 divided by 25 is 6 with a remainder of 7.
The number 6 becomes the next digit in our result. 
Result so far: 166.0
If we subtract 150 from 157, we get 7.
Fetch the next digit (8) from the dividend, attach it to 7 and continue: 78 / 25

Moving on to step 5:
25 can be fit into 78 3 times, resulting in a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 1663.0
Deduct 75 from 78 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.

Advancing to step 6:
If we divide 30 by 25, we get 1 and a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 1663.1
If we subtract 25 from 30, we 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.

On to step 7:
25 goes into 50 2 times with a remainder of 0.
Use 2 as the next digit of our solution. 
Result so far: 1663.12
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.

Step 8:
If we divide 0 by 25, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 1663.12
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.

Moving on to step 9:
0 divided by 25 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 1663.12
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.

The final result is 1663.12 with a remainder of 0.0.