We look at the division of 665838 by 61 
We want to divide 665838 by 61.

Step 1:
The number 61 fits into 6 0 times, leaving a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 61

Moving on to step 2:
If we divide 66 by 61, we get 1 and a remainder of 5.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 61 from 66, we get 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 61

On to step 3:
55 divided by 61 is 0 with a remainder of 55.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Subtract 0 from 55 to get 55.
Fetch the next digit (8) from the dividend, attach it to 55 and continue: 558 / 61

Moving on to step 4:
61 goes into 558 9 times with a remainder of 9.
Record the quotient 9 as the next digit in the result. 
Result so far: 109.0
Subtract 549 from 558 to get 9.
Bring next digit (3) of the dividend behind the 9 and repeat the process: 93 / 61

Moving on to step 5:
93 divided by 61 is 1 with a remainder of 32.
Write down 1 as next digit of the result. 
Result so far: 1091.0
Subtract 61 from 93 to get 32.
Include the next digit (8) from the dividend after 32, then repeat: 328 / 61

Advancing to step 6:
When dividing 328 by 61, we get 5 with a remainder of 23.
The number 5 becomes the next digit in our result. 
Result so far: 10915.0
Subtract 305 from 328 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 7:
When dividing 230 by 61, we get 3 with a remainder of 47.
Write down 3 as next digit of the result. 
Result so far: 10915.3
If we subtract 183 from 230, we get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Let's proceed to step 8:
When dividing 470 by 61, we get 7 with a remainder of 43.
Write down 7 as next digit of the result. 
Result so far: 10915.37
Subtracting 427 from 470 leaves us with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 9:
61 can be fit into 430 7 times, resulting in a remainder of 3.
The next digit of our result is 7. 
Result so far: 10915.377
If we subtract 427 from 430, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

In conclusion, the division gives 10915.377 with a balance of 0.0003.