We're dividing 634765 by 41 
We want to divide 634765 by 41.

Going ahead to step 1:
41 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 41

Step 2:
41 can be fit into 63 1 times, resulting in a remainder of 22.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 41 away from 63, we end up with 22.
Include the next digit (4) from the dividend after 22, then repeat: 224 / 41

Advancing to step 3:
224 divided by 41 is 5 with a remainder of 19.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
If we subtract 205 from 224, we get 19.
Append the next digit (7) from the dividend to 19 and continue with: 197 / 41

Moving on to step 4:
If we divide 197 by 41, we get 4 and a remainder of 33.
Record the quotient 4 as the next digit in the result. 
Result so far: 154.0
If we subtract 164 from 197, we get 33.
Grab the next digit (6) from the dividend, add it to 33, then carry on: 336 / 41

On to step 5:
41 goes into 336 8 times with a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 1548.0
If we take 328 away from 336, we end up with 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 41

Let's proceed to step 6:
41 goes into 85 2 times with a remainder of 3.
The next digit of our result is 2. 
Result so far: 15482.0
Deduct 82 from 85 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.

Moving on to step 7:
If we divide 30 by 41, we get 0 and a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 15482.0
The remainder is 30 after subtracting 0 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 8:
41 goes into 300 7 times with a remainder of 13.
The next digit of our result is 7. 
Result so far: 15482.07
The remainder is 13 after subtracting 287 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 9:
41 goes into 130 3 times with a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 15482.073
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.

Going ahead to step 10:
41 goes into 70 1 times with a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 15482.0731
If we subtract 41 from 70, we 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.

Let's proceed to step 11:
If we divide 290 by 41, we get 7 and a remainder of 3.
The next digit of our result is 7. 
Result so far: 15482.07317
Deduct 287 from 290 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.

Let's proceed to step 12:
30 divided by 41 is 0 with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 15482.07317
Subtract 0 from 30 to get 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:
The number 41 fits into 300 7 times, leaving a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 15482.0731707
The remainder is 13 after subtracting 287 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 14:
41 can be fit into 130 3 times, resulting in a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 15482.07317073
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.

After the division, we end up with 15482.07317073 and a remainder of 7e-09.