665971 ÷ 61 
Our goal is to divide 665971 by 61.

Step 1:
The number 61 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 61

Advancing to step 2:
61 can be fit into 66 1 times, resulting in a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 61 from 66 leaves us with 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 61

Step 3:
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: 10.0
If we subtract 0 from 55, we get 55.
Append the next digit (9) from the dividend to 55 and continue with: 559 / 61

On to step 4:
559 divided by 61 is 9 with a remainder of 10.
Write down 9 as next digit of the result. 
Result so far: 109.0
If we subtract 549 from 559, we get 10.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 61

Advancing to step 5:
61 can be fit into 107 1 times, resulting in a remainder of 46.
Record the quotient 1 as the next digit in the result. 
Result so far: 1091.0
The remainder is 46 after subtracting 61 from 107.
Include the next digit (1) from the dividend after 46, then repeat: 461 / 61

On to step 6:
The number 61 fits into 461 7 times, leaving a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 10917.0
Subtract 427 from 461 to get 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 7:
61 goes into 340 5 times with a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 10917.5
The remainder is 35 after subtracting 305 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 8:
350 divided by 61 is 5 with a remainder of 45.
Record the quotient 5 as the next digit in the result. 
Result so far: 10917.55
Deduct 305 from 350 and we're left with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

The final outcome is 10917.55, with a leftover of 0.045.