71766291 ÷ 681 
We want to figure out the number of times 71766291 can be divided by 681.

On to step 1:
The number 681 fits into 7 0 times, leaving a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Append the next digit (1) from the dividend to 7 and continue with: 71 / 681

On to step 2:
681 goes into 71 0 times with a remainder of 71.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 71 to get 71.
Grab the next digit (7) from the dividend, add it to 71, then carry on: 717 / 681

Step 3:
681 goes into 717 1 times with a remainder of 36.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 36 after subtracting 681 from 717.
Take the next digit (6) from the dividend and append it to 36, then repeat: 366 / 681

Going ahead to step 4:
If we divide 366 by 681, we get 0 and a remainder of 366.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Deduct 0 from 366 and we're left with 366.
Include the next digit (6) from the dividend after 366, then repeat: 3666 / 681

Moving on to step 5:
3666 divided by 681 is 5 with a remainder of 261.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
If we subtract 3405 from 3666, we get 261.
Bring next digit (2) of the dividend behind the 261 and repeat the process: 2612 / 681

Let's proceed to step 6:
681 can be fit into 2612 3 times, resulting in a remainder of 569.
Use 3 as the next digit of our solution. 
Result so far: 1053.0
Subtracting 2043 from 2612 leaves us with 569.
Grab the next digit (9) from the dividend, add it to 569, then carry on: 5699 / 681

On to step 7:
When dividing 5699 by 681, we get 8 with a remainder of 251.
The next digit of our result is 8. 
Result so far: 10538.0
If we subtract 5448 from 5699, we get 251.
Bring next digit (1) of the dividend behind the 251 and repeat the process: 2511 / 681

Advancing to step 8:
681 goes into 2511 3 times with a remainder of 468.
Write down 3 as next digit of the result. 
Result so far: 105383.0
Subtracting 2043 from 2511 leaves us with 468.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4680, and continue the process.

Step 9:
681 can be fit into 4680 6 times, resulting in a remainder of 594.
Write down 6 as next digit of the result. 
Result so far: 105383.6
If we take 4086 away from 4680, we end up with 594.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5940, and continue the process.

Step 10:
When dividing 5940 by 681, we get 8 with a remainder of 492.
Record the quotient 8 as the next digit in the result. 
Result so far: 105383.68
Subtract 5448 from 5940 to get 492.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4920, and continue the process.

Step 11:
4920 divided by 681 is 7 with a remainder of 153.
The next digit of our result is 7. 
Result so far: 105383.687
The remainder is 153 after subtracting 4767 from 4920.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1530, and continue the process.

Going ahead to step 12:
681 goes into 1530 2 times with a remainder of 168.
The next digit of our result is 2. 
Result so far: 105383.6872
The remainder is 168 after subtracting 1362 from 1530.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1680, and continue the process.

Let's proceed to step 13:
When dividing 1680 by 681, we get 2 with a remainder of 318.
The next digit of our result is 2. 
Result so far: 105383.68722
If we take 1362 away from 1680, we end up with 318.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3180, and continue the process.

Our division results in 105383.68722 with a remaining 0.000318.