We're dividing 559996 by 61 
We want to figure out the number of times 559996 can be divided by 61.

Advancing to step 1:
If we divide 5 by 61, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 61

Moving on to step 2:
If we divide 55 by 61, we get 0 and a remainder of 55.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 55 leaves us with 55.
Include the next digit (9) from the dividend after 55, then repeat: 559 / 61

Let's proceed to step 3:
61 goes into 559 9 times with a remainder of 10.
Use 9 as the next digit of our solution. 
Result so far: 9.0
Subtracting 549 from 559 leaves us with 10.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 61

Step 4:
When dividing 109 by 61, we get 1 with a remainder of 48.
Write down 1 as next digit of the result. 
Result so far: 91.0
If we subtract 61 from 109, we get 48.
Grab the next digit (9) from the dividend, add it to 48, then carry on: 489 / 61

Going ahead to step 5:
489 divided by 61 is 8 with a remainder of 1.
The next digit of our result is 8. 
Result so far: 918.0
Deduct 488 from 489 and we're left with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 61

Let's proceed to step 6:
61 can be fit into 16 0 times, resulting in a remainder of 16.
Put 0 as the next digit of the answer. 
Result so far: 9180.0
If we take 0 away from 16, 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.

Advancing to step 7:
61 goes into 160 2 times with a remainder of 38.
Put 2 as the next digit of the answer. 
Result so far: 9180.2
Subtracting 122 from 160 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 8:
61 goes into 380 6 times with a remainder of 14.
Record the quotient 6 as the next digit in the result. 
Result so far: 9180.26
Subtract 366 from 380 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 9:
If we divide 140 by 61, we get 2 and a remainder of 18.
Put 2 as the next digit of the answer. 
Result so far: 9180.262
Subtract 122 from 140 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 10:
The number 61 fits into 180 2 times, leaving a remainder of 58.
The next digit of our result is 2. 
Result so far: 9180.2622
Deduct 122 from 180 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

The quotient of the division is 9180.2622, and the remainder is 0.00058.