We're dividing 415194 by 25 
We're looking to find how many times 25 goes into 415194.

Moving on to step 1:
If we divide 4 by 25, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 25

Advancing to step 2:
If we divide 41 by 25, we get 1 and a remainder of 16.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 25 from 41 to get 16.
Fetch the next digit (5) from the dividend, attach it to 16 and continue: 165 / 25

Going ahead to step 3:
When dividing 165 by 25, we get 6 with a remainder of 15.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.0
If we take 150 away from 165, we end up with 15.
Include the next digit (1) from the dividend after 15, then repeat: 151 / 25

Going ahead to step 4:
25 goes into 151 6 times with a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 166.0
If we subtract 150 from 151, we get 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 25

Step 5:
25 goes into 19 0 times with a remainder of 19.
Put 0 as the next digit of the answer. 
Result so far: 1660.0
Subtract 0 from 19 to get 19.
Append the next digit (4) from the dividend to 19 and continue with: 194 / 25

On to step 6:
When dividing 194 by 25, we get 7 with a remainder of 19.
Put 7 as the next digit of the answer. 
Result so far: 16607.0
The remainder is 19 after subtracting 175 from 194.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
The number 25 fits into 190 7 times, leaving a remainder of 15.
Write down 7 as next digit of the result. 
Result so far: 16607.7
Deduct 175 from 190 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 8:
25 goes into 150 6 times with a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 16607.76
Subtract 150 from 150 to 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.

Going ahead to step 9:
25 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 16607.76
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.

Advancing to step 10:
The number 25 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 16607.76
Subtract 0 from 0 to 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.

The quotient of the division is 16607.76, and the remainder is 0.0.