We're dividing 555541 by 61 
We want to figure out the number of times 555541 can be divided by 61.

Step 1:
If we divide 5 by 61, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 61

Advancing to step 2:
If we divide 55 by 61, we get 0 and a remainder of 55.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Append the next digit (5) from the dividend to 55 and continue with: 555 / 61

Step 3:
61 can be fit into 555 9 times, resulting in a remainder of 6.
Write down 9 as next digit of the result. 
Result so far: 9.0
If we take 549 away from 555, we end up with 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 61

Moving on to step 4:
When dividing 65 by 61, we get 1 with a remainder of 4.
The next digit of our result is 1. 
Result so far: 91.0
If we take 61 away from 65, we end up with 4.
Append the next digit (4) from the dividend to 4 and continue with: 44 / 61

Advancing to step 5:
When dividing 44 by 61, we get 0 with a remainder of 44.
Record the quotient 0 as the next digit in the result. 
Result so far: 910.0
Deduct 0 from 44 and we're left with 44.
Grab the next digit (1) from the dividend, add it to 44, then carry on: 441 / 61

Going ahead to step 6:
When dividing 441 by 61, we get 7 with a remainder of 14.
Write down 7 as next digit of the result. 
Result so far: 9107.0
Subtract 427 from 441 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.

On to step 7:
The number 61 fits into 140 2 times, leaving a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 9107.2
Subtracting 122 from 140 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 8:
61 goes into 180 2 times with a remainder of 58.
Record the quotient 2 as the next digit in the result. 
Result so far: 9107.22
If we take 122 away from 180, we end up 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 final result is 9107.22 with a remainder of 0.058.