We look at the division of 637914 by 41 
We're looking to find how many times 41 goes into 637914.

On to step 1:
The number 41 fits into 6 0 times, leaving a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 41

Moving on to step 2:
41 can be fit into 63 1 times, resulting in a remainder of 22.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 41 from 63, we get 22.
Grab the next digit (7) from the dividend, add it to 22, then carry on: 227 / 41

Step 3:
When dividing 227 by 41, we get 5 with a remainder of 22.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
The remainder is 22 after subtracting 205 from 227.
Grab the next digit (9) from the dividend, add it to 22, then carry on: 229 / 41

On to step 4:
41 can be fit into 229 5 times, resulting in a remainder of 24.
Put 5 as the next digit of the answer. 
Result so far: 155.0
If we take 205 away from 229, we end up with 24.
Bring next digit (1) of the dividend behind the 24 and repeat the process: 241 / 41

Step 5:
241 divided by 41 is 5 with a remainder of 36.
Put 5 as the next digit of the answer. 
Result so far: 1555.0
If we take 205 away from 241, we end up with 36.
Grab the next digit (4) from the dividend, add it to 36, then carry on: 364 / 41

Going ahead to step 6:
The number 41 fits into 364 8 times, leaving a remainder of 36.
The next digit of our result is 8. 
Result so far: 15558.0
Subtract 328 from 364 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 7:
The number 41 fits into 360 8 times, leaving a remainder of 32.
The number 8 becomes the next digit in our result. 
Result so far: 15558.8
Deduct 328 from 360 and we're left 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.

Going ahead to step 8:
When dividing 320 by 41, we get 7 with a remainder of 33.
Use 7 as the next digit of our solution. 
Result so far: 15558.87
If we take 287 away from 320, we end up 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 9:
330 divided by 41 is 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 15558.878
Subtracting 328 from 330 leaves us 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.

On to step 10:
20 divided by 41 is 0 with a remainder of 20.
Write down 0 as next digit of the result. 
Result so far: 15558.878
The remainder is 20 after subtracting 0 from 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 11:
200 divided by 41 is 4 with a remainder of 36.
Use 4 as the next digit of our solution. 
Result so far: 15558.87804
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.

On to step 12:
When dividing 360 by 41, we get 8 with a remainder of 32.
The next digit of our result is 8. 
Result so far: 15558.878048
If we subtract 328 from 360, we get 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 13:
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: 15558.8780487
If we take 287 away from 320, we end up 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.

Let's proceed to step 14:
When dividing 330 by 41, we get 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 15558.87804878
If we subtract 328 from 330, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 15558.87804878 and a remainder of 2e-09.