We're dividing 108271 by 61 
We want to figure out the number of times 108271 can be divided by 61.

Step 1:
When dividing 1 by 61, we get 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 (0) from the dividend and append it to 1, then repeat: 10 / 61

Step 2:
The number 61 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Append the next digit (8) from the dividend to 10 and continue with: 108 / 61

Going ahead to step 3:
If we divide 108 by 61, we get 1 and a remainder of 47.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 61 from 108, we get 47.
Fetch the next digit (2) from the dividend, attach it to 47 and continue: 472 / 61

Going ahead to step 4:
472 divided by 61 is 7 with a remainder of 45.
The number 7 becomes the next digit in our result. 
Result so far: 17.0
Deduct 427 from 472 and we're left with 45.
Bring next digit (7) of the dividend behind the 45 and repeat the process: 457 / 61

On to step 5:
61 can be fit into 457 7 times, resulting in a remainder of 30.
Write down 7 as next digit of the result. 
Result so far: 177.0
Deduct 427 from 457 and we're left with 30.
Bring next digit (1) of the dividend behind the 30 and repeat the process: 301 / 61

Let's proceed to step 6:
The number 61 fits into 301 4 times, leaving a remainder of 57.
Record the quotient 4 as the next digit in the result. 
Result so far: 1774.0
Deduct 244 from 301 and we're left with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

On to step 7:
When dividing 570 by 61, we get 9 with a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 1774.9
Deduct 549 from 570 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Step 8:
The number 61 fits into 210 3 times, leaving a remainder of 27.
Use 3 as the next digit of our solution. 
Result so far: 1774.93
Deduct 183 from 210 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 9:
When dividing 270 by 61, we get 4 with a remainder of 26.
Put 4 as the next digit of the answer. 
Result so far: 1774.934
The remainder is 26 after subtracting 244 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 10:
If we divide 260 by 61, we get 4 and a remainder of 16.
Write down 4 as next digit of the result. 
Result so far: 1774.9344
If we take 244 away from 260, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

In conclusion, the division gives 1774.9344 with a balance of 0.00016.