We're dividing 403634 by 61 
We want to divide 403634 by 61.

Step 1:
When dividing 4 by 61, we get 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 61

Going ahead to step 2:
61 goes into 40 0 times with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 40 after subtracting 0 from 40.
Take the next digit (3) from the dividend and append it to 40, then repeat: 403 / 61

Step 3:
61 can be fit into 403 6 times, resulting in a remainder of 37.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we take 366 away from 403, we end up with 37.
Include the next digit (6) from the dividend after 37, then repeat: 376 / 61

Step 4:
61 goes into 376 6 times with a remainder of 10.
The next digit of our result is 6. 
Result so far: 66.0
If we take 366 away from 376, we end up with 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 61

Going ahead to step 5:
61 goes into 103 1 times with a remainder of 42.
Put 1 as the next digit of the answer. 
Result so far: 661.0
Subtracting 61 from 103 leaves us with 42.
Fetch the next digit (4) from the dividend, attach it to 42 and continue: 424 / 61

Going ahead to step 6:
424 divided by 61 is 6 with a remainder of 58.
Use 6 as the next digit of our solution. 
Result so far: 6616.0
If we subtract 366 from 424, we get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 7:
When dividing 580 by 61, we get 9 with a remainder of 31.
Put 9 as the next digit of the answer. 
Result so far: 6616.9
The remainder is 31 after subtracting 549 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 8:
61 can be fit into 310 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 6616.95
Deduct 305 from 310 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 9:
If we divide 50 by 61, we get 0 and a remainder of 50.
The next digit of our result is 0. 
Result so far: 6616.95
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 10:
500 divided by 61 is 8 with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 6616.9508
Deduct 488 from 500 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 11:
The number 61 fits into 120 1 times, leaving a remainder of 59.
Put 1 as the next digit of the answer. 
Result so far: 6616.95081
If we subtract 61 from 120, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 12:
The number 61 fits into 590 9 times, leaving a remainder of 41.
The number 9 becomes the next digit in our result. 
Result so far: 6616.950819
Deduct 549 from 590 and we're left with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Going ahead to step 13:
61 goes into 410 6 times with a remainder of 44.
Use 6 as the next digit of our solution. 
Result so far: 6616.9508196
If we subtract 366 from 410, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 14:
The number 61 fits into 440 7 times, leaving a remainder of 13.
Write down 7 as next digit of the result. 
Result so far: 6616.95081967
Subtracting 427 from 440 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.

In conclusion, the division gives 6616.95081967 with a balance of 1.3e-08.