We look at the division of 415678 by 41 
We want to divide 415678 by 41.

Advancing to step 1:
41 goes into 4 0 times with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 41

Moving on to step 2:
41 goes into 41 1 times with a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 41 from 41, we get 0.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 41

Step 3:
If we divide 5 by 41, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtract 0 from 5 to get 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 41

Advancing to step 4:
The number 41 fits into 56 1 times, leaving a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 101.0
Subtracting 41 from 56 leaves us with 15.
Include the next digit (7) from the dividend after 15, then repeat: 157 / 41

On to step 5:
If we divide 157 by 41, we get 3 and a remainder of 34.
The next digit of our result is 3. 
Result so far: 1013.0
Deduct 123 from 157 and we're left with 34.
Take the next digit (8) from the dividend and append it to 34, then repeat: 348 / 41

On to step 6:
When dividing 348 by 41, we get 8 with a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 10138.0
The remainder is 20 after subtracting 328 from 348.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 7:
41 goes into 200 4 times with a remainder of 36.
The next digit of our result is 4. 
Result so far: 10138.4
Deduct 164 from 200 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 8:
When dividing 360 by 41, we get 8 with a remainder of 32.
The number 8 becomes the next digit in our result. 
Result so far: 10138.48
If we take 328 away from 360, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 9:
If we divide 320 by 41, we get 7 and a remainder of 33.
Write down 7 as next digit of the result. 
Result so far: 10138.487
Deduct 287 from 320 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 10:
The number 41 fits into 330 8 times, leaving a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 10138.4878
If we take 328 away from 330, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 11:
20 divided by 41 is 0 with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 10138.4878
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 12:
The number 41 fits into 200 4 times, leaving a remainder of 36.
Write down 4 as next digit of the result. 
Result so far: 10138.487804
The remainder is 36 after subtracting 164 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 13:
The number 41 fits into 360 8 times, leaving a remainder of 32.
The next digit of our result is 8. 
Result so far: 10138.4878048
The remainder is 32 after subtracting 328 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 14:
41 can be fit into 320 7 times, resulting in a remainder of 33.
The next digit of our result is 7. 
Result so far: 10138.48780487
Subtract 287 from 320 to get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

The final result is 10138.48780487 with a remainder of 3.3e-08.