515823 ÷ 61 
Let's see how many times 61 fits into 515823.

On to step 1:
When dividing 5 by 61, we get 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 61

Advancing to step 2:
51 divided by 61 is 0 with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Include the next digit (5) from the dividend after 51, then repeat: 515 / 61

Let's proceed to step 3:
515 divided by 61 is 8 with a remainder of 27.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
If we take 488 away from 515, we end up with 27.
Append the next digit (8) from the dividend to 27 and continue with: 278 / 61

Step 4:
61 can be fit into 278 4 times, resulting in a remainder of 34.
Put 4 as the next digit of the answer. 
Result so far: 84.0
Subtracting 244 from 278 leaves us with 34.
Grab the next digit (2) from the dividend, add it to 34, then carry on: 342 / 61

On to step 5:
342 divided by 61 is 5 with a remainder of 37.
The number 5 becomes the next digit in our result. 
Result so far: 845.0
The remainder is 37 after subtracting 305 from 342.
Take the next digit (3) from the dividend and append it to 37, then repeat: 373 / 61

On to step 6:
373 divided by 61 is 6 with a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 8456.0
Deduct 366 from 373 and we're left 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.

Let's proceed to step 7:
If we divide 70 by 61, we get 1 and a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 8456.1
Deduct 61 from 70 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 8:
When dividing 90 by 61, we get 1 with a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 8456.11
Subtracting 61 from 90 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

In conclusion, the division gives 8456.11 with a balance of 0.029.