We're dividing 261633 by 61 
We want to figure out the number of times 261633 can be divided by 61.

Step 1:
When dividing 2 by 61, we get 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 61

Let's proceed to step 2:
When dividing 26 by 61, we get 0 with a remainder of 26.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 26, we get 26.
Take the next digit (1) from the dividend and append it to 26, then repeat: 261 / 61

Going ahead to step 3:
261 divided by 61 is 4 with a remainder of 17.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
Subtract 244 from 261 to get 17.
Grab the next digit (6) from the dividend, add it to 17, then carry on: 176 / 61

On to step 4:
61 goes into 176 2 times with a remainder of 54.
Put 2 as the next digit of the answer. 
Result so far: 42.0
Subtracting 122 from 176 leaves us with 54.
Grab the next digit (3) from the dividend, add it to 54, then carry on: 543 / 61

Going ahead to step 5:
61 can be fit into 543 8 times, resulting in a remainder of 55.
The next digit of our result is 8. 
Result so far: 428.0
Subtracting 488 from 543 leaves us with 55.
Fetch the next digit (3) from the dividend, attach it to 55 and continue: 553 / 61

Moving on to step 6:
61 can be fit into 553 9 times, resulting in a remainder of 4.
Record the quotient 9 as the next digit in the result. 
Result so far: 4289.0
If we take 549 away from 553, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 7:
When dividing 40 by 61, we get 0 with a remainder of 40.
The next digit of our result is 0. 
Result so far: 4289.0
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 8:
61 can be fit into 400 6 times, resulting in a remainder of 34.
Put 6 as the next digit of the answer. 
Result so far: 4289.06
Subtracting 366 from 400 leaves us 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.

Moving on to step 9:
61 can be fit into 340 5 times, resulting in a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 4289.065
If we take 305 away from 340, we end up 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.

Step 10:
350 divided by 61 is 5 with a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 4289.0655
The remainder is 45 after subtracting 305 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

In conclusion, the division gives 4289.0655 with a balance of 0.00045.