We're dividing 416571 by 25 
We want to figure out the number of times 416571 can be divided by 25.

Going ahead to step 1:
25 can be fit into 4 0 times, resulting in a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 25

Step 2:
When dividing 41 by 25, we get 1 with a remainder of 16.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 16 after subtracting 25 from 41.
Append the next digit (6) from the dividend to 16 and continue with: 166 / 25

On to step 3:
The number 25 fits into 166 6 times, leaving a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 16.0
The remainder is 16 after subtracting 150 from 166.
Fetch the next digit (5) from the dividend, attach it to 16 and continue: 165 / 25

Step 4:
When dividing 165 by 25, we get 6 with a remainder of 15.
Write down 6 as next digit of the result. 
Result so far: 166.0
Subtracting 150 from 165 leaves us with 15.
Grab the next digit (7) from the dividend, add it to 15, then carry on: 157 / 25

Advancing to step 5:
25 goes into 157 6 times with a remainder of 7.
Write down 6 as next digit of the result. 
Result so far: 1666.0
If we subtract 150 from 157, we get 7.
Append the next digit (1) from the dividend to 7 and continue with: 71 / 25

On to step 6:
When dividing 71 by 25, we get 2 with a remainder of 21.
Write down 2 as next digit of the result. 
Result so far: 16662.0
Deduct 50 from 71 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 7:
25 can be fit into 210 8 times, resulting in a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 16662.8
Deduct 200 from 210 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
When dividing 100 by 25, we get 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 16662.84
Subtracting 100 from 100 leaves us 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.

Moving on to step 9:
The number 25 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 16662.84
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:
If we divide 0 by 25, we get 0 and a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 16662.84
Subtracting 0 from 0 leaves us 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 outcome is 16662.84, with a leftover of 0.0.