25613 ÷ 41 
Our goal is to divide 25613 by 41.

Step 1:
41 can be fit into 2 0 times, resulting in a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 41

On to step 2:
25 divided by 41 is 0 with a remainder of 25.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 25 after subtracting 0 from 25.
Fetch the next digit (6) from the dividend, attach it to 25 and continue: 256 / 41

Advancing to step 3:
The number 41 fits into 256 6 times, leaving a remainder of 10.
The next digit of our result is 6. 
Result so far: 6.0
Subtract 246 from 256 to get 10.
Take the next digit (1) from the dividend and append it to 10, then repeat: 101 / 41

Let's proceed to step 4:
When dividing 101 by 41, we get 2 with a remainder of 19.
Use 2 as the next digit of our solution. 
Result so far: 62.0
If we subtract 82 from 101, we get 19.
Bring next digit (3) of the dividend behind the 19 and repeat the process: 193 / 41

Step 5:
41 goes into 193 4 times with a remainder of 29.
Use 4 as the next digit of our solution. 
Result so far: 624.0
If we take 164 away from 193, we end up with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Advancing to step 6:
If we divide 290 by 41, we get 7 and a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 624.7
Subtracting 287 from 290 leaves us 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.

Going ahead to step 7:
The number 41 fits into 30 0 times, leaving a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 624.7
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 8:
The number 41 fits into 300 7 times, leaving a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 624.707
If we take 287 away from 300, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 9:
41 goes into 130 3 times with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 624.7073
If we take 123 away from 130, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 10:
The number 41 fits into 70 1 times, leaving a remainder of 29.
Write down 1 as next digit of the result. 
Result so far: 624.70731
Subtract 41 from 70 to get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Advancing to step 11:
41 can be fit into 290 7 times, resulting in a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 624.707317
Subtracting 287 from 290 leaves us 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 12:
41 goes into 30 0 times with a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 624.707317
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 13:
If we divide 300 by 41, we get 7 and a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 624.70731707
Subtract 287 from 300 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final result is 624.70731707 with a remainder of 1.3e-08.