We look at the division of 681577 by 61 
We're looking to find how many times 61 goes into 681577.

Moving on to step 1:
If we divide 6 by 61, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Include the next digit (8) from the dividend after 6, then repeat: 68 / 61

Moving on to step 2:
When dividing 68 by 61, we get 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 61 from 68 and we're left with 7.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 61

On to step 3:
71 divided by 61 is 1 with a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
Subtract 61 from 71 to get 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 61

Let's proceed to step 4:
105 divided by 61 is 1 with a remainder of 44.
Write down 1 as next digit of the result. 
Result so far: 111.0
If we subtract 61 from 105, we get 44.
Include the next digit (7) from the dividend after 44, then repeat: 447 / 61

Let's proceed to step 5:
447 divided by 61 is 7 with a remainder of 20.
Put 7 as the next digit of the answer. 
Result so far: 1117.0
Subtracting 427 from 447 leaves us with 20.
Include the next digit (7) from the dividend after 20, then repeat: 207 / 61

Moving on to step 6:
61 goes into 207 3 times with a remainder of 24.
Write down 3 as next digit of the result. 
Result so far: 11173.0
If we subtract 183 from 207, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 7:
If we divide 240 by 61, we get 3 and a remainder of 57.
The next digit of our result is 3. 
Result so far: 11173.3
Subtracting 183 from 240 leaves us with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Going ahead to step 8:
The number 61 fits into 570 9 times, leaving a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 11173.39
Subtracting 549 from 570 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 9:
The number 61 fits into 210 3 times, leaving a remainder of 27.
Use 3 as the next digit of our solution. 
Result so far: 11173.393
Deduct 183 from 210 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Moving on to step 10:
The number 61 fits into 270 4 times, leaving a remainder of 26.
Write down 4 as next digit of the result. 
Result so far: 11173.3934
Subtracting 244 from 270 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 11:
61 goes into 260 4 times with a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 11173.39344
Subtract 244 from 260 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final outcome is 11173.39344, with a leftover of 1.6e-05.