We look at the division of 414103 by 41 
We're looking to find how many times 41 goes into 414103.

Moving on to step 1:
When dividing 4 by 41, we get 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 41

Step 2:
The number 41 fits into 41 1 times, leaving a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 41 from 41 to get 0.
Fetch the next digit (4) from the dividend, attach it to 0 and continue: 4 / 41

Step 3:
41 can be fit into 4 0 times, resulting in a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 10.0
Deduct 0 from 4 and we're left with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 41

Advancing to step 4:
41 divided by 41 is 1 with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 101.0
Deduct 41 from 41 and we're left with 0.
Append the next digit (0) from the dividend to 0 and continue with: 0 / 41

Let's proceed to step 5:
If we divide 0 by 41, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 1010.0
If we subtract 0 from 0, we get 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 41

Going ahead to step 6:
41 goes into 3 0 times with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 10100.0
Deduct 0 from 3 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.

On to step 7:
41 can be fit into 30 0 times, resulting in a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 10100.0
Deduct 0 from 30 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
If we divide 300 by 41, we get 7 and a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 10100.07
Subtracting 287 from 300 leaves us 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.

Step 9:
41 can be fit into 130 3 times, resulting in a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 10100.073
Subtracting 123 from 130 leaves us 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.

Advancing to step 10:
41 goes into 70 1 times with a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 10100.0731
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.

Moving on to step 11:
41 can be fit into 290 7 times, resulting in a remainder of 3.
The next digit of our result is 7. 
Result so far: 10100.07317
Subtract 287 from 290 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 12:
41 can be fit into 30 0 times, resulting in a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 10100.07317
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 13:
When dividing 300 by 41, we get 7 with a remainder of 13.
Write down 7 as next digit of the result. 
Result so far: 10100.0731707
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.

Step 14:
The number 41 fits into 130 3 times, leaving a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 10100.07317073
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.

Our division results in 10100.07317073 with a remaining 7e-09.