We're dividing 115629 by 61 
We want to divide 115629 by 61.

Moving on to step 1:
1 divided by 61 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 61

Advancing to step 2:
61 goes into 11 0 times with a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 11 and we're left with 11.
Fetch the next digit (5) from the dividend, attach it to 11 and continue: 115 / 61

On to step 3:
The number 61 fits into 115 1 times, leaving a remainder of 54.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 61 away from 115, we end up with 54.
Fetch the next digit (6) from the dividend, attach it to 54 and continue: 546 / 61

On to step 4:
The number 61 fits into 546 8 times, leaving a remainder of 58.
Write down 8 as next digit of the result. 
Result so far: 18.0
If we subtract 488 from 546, we get 58.
Take the next digit (2) from the dividend and append it to 58, then repeat: 582 / 61

On to step 5:
When dividing 582 by 61, we get 9 with a remainder of 33.
The number 9 becomes the next digit in our result. 
Result so far: 189.0
Subtract 549 from 582 to get 33.
Append the next digit (9) from the dividend to 33 and continue with: 339 / 61

Step 6:
The number 61 fits into 339 5 times, leaving a remainder of 34.
Record the quotient 5 as the next digit in the result. 
Result so far: 1895.0
Deduct 305 from 339 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 7:
If we divide 340 by 61, we get 5 and a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 1895.5
Subtracting 305 from 340 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 8:
If we divide 350 by 61, we get 5 and a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 1895.55
If we take 305 away from 350, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

The final result is 1895.55 with a remainder of 0.045.