We look at the division of 645631 by 41 
We're looking to find how many times 41 goes into 645631.

Step 1:
41 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 41

Step 2:
If we divide 64 by 41, we get 1 and a remainder of 23.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 41 from 64, we get 23.
Take the next digit (5) from the dividend and append it to 23, then repeat: 235 / 41

Going ahead to step 3:
When dividing 235 by 41, we get 5 with a remainder of 30.
The next digit of our result is 5. 
Result so far: 15.0
If we take 205 away from 235, we end up with 30.
Append the next digit (6) from the dividend to 30 and continue with: 306 / 41

Step 4:
The number 41 fits into 306 7 times, leaving a remainder of 19.
Write down 7 as next digit of the result. 
Result so far: 157.0
Deduct 287 from 306 and we're left with 19.
Fetch the next digit (3) from the dividend, attach it to 19 and continue: 193 / 41

Advancing to step 5:
The number 41 fits into 193 4 times, leaving a remainder of 29.
Record the quotient 4 as the next digit in the result. 
Result so far: 1574.0
Subtracting 164 from 193 leaves us with 29.
Take the next digit (1) from the dividend and append it to 29, then repeat: 291 / 41

On to step 6:
291 divided by 41 is 7 with a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 15747.0
If we take 287 away from 291, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 7:
40 divided by 41 is 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 15747.0
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 8:
If we divide 400 by 41, we get 9 and a remainder of 31.
Use 9 as the next digit of our solution. 
Result so far: 15747.09
The remainder is 31 after subtracting 369 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 9:
The number 41 fits into 310 7 times, leaving a remainder of 23.
The next digit of our result is 7. 
Result so far: 15747.097
If we subtract 287 from 310, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 10:
When dividing 230 by 41, we get 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 15747.0975
The remainder is 25 after subtracting 205 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 11:
41 can be fit into 250 6 times, resulting in a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 15747.09756
Deduct 246 from 250 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 12:
40 divided by 41 is 0 with a remainder of 40.
The next digit of our result is 0. 
Result so far: 15747.09756
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 13:
400 divided by 41 is 9 with a remainder of 31.
Use 9 as the next digit of our solution. 
Result so far: 15747.0975609
Deduct 369 from 400 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 14:
When dividing 310 by 41, we get 7 with a remainder of 23.
Use 7 as the next digit of our solution. 
Result so far: 15747.09756097
Subtract 287 from 310 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

After the division, we end up with 15747.09756097 and a remainder of 2.3e-08.