5745871 ÷ 766 
Our goal is to divide 5745871 by 766.

On to step 1:
5 divided by 766 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 766

Going ahead to step 2:
57 divided by 766 is 0 with a remainder of 57.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 57 to get 57.
Bring next digit (4) of the dividend behind the 57 and repeat the process: 574 / 766

Step 3:
766 can be fit into 574 0 times, resulting in a remainder of 574.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 574 after subtracting 0 from 574.
Append the next digit (5) from the dividend to 574 and continue with: 5745 / 766

Advancing to step 4:
The number 766 fits into 5745 7 times, leaving a remainder of 383.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtract 5362 from 5745 to get 383.
Fetch the next digit (8) from the dividend, attach it to 383 and continue: 3838 / 766

On to step 5:
If we divide 3838 by 766, we get 5 and a remainder of 8.
Use 5 as the next digit of our solution. 
Result so far: 75.0
Subtracting 3830 from 3838 leaves us with 8.
Include the next digit (7) from the dividend after 8, then repeat: 87 / 766

Let's proceed to step 6:
766 can be fit into 87 0 times, resulting in a remainder of 87.
Put 0 as the next digit of the answer. 
Result so far: 750.0
Deduct 0 from 87 and we're left with 87.
Take the next digit (1) from the dividend and append it to 87, then repeat: 871 / 766

On to step 7:
If we divide 871 by 766, we get 1 and a remainder of 105.
The number 1 becomes the next digit in our result. 
Result so far: 7501.0
The remainder is 105 after subtracting 766 from 871.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1050, and continue the process.

Let's proceed to step 8:
766 can be fit into 1050 1 times, resulting in a remainder of 284.
The number 1 becomes the next digit in our result. 
Result so far: 7501.1
If we subtract 766 from 1050, we get 284.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2840, and continue the process.

Let's proceed to step 9:
The number 766 fits into 2840 3 times, leaving a remainder of 542.
The number 3 becomes the next digit in our result. 
Result so far: 7501.13
The remainder is 542 after subtracting 2298 from 2840.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5420, and continue the process.

Going ahead to step 10:
When dividing 5420 by 766, we get 7 with a remainder of 58.
The next digit of our result is 7. 
Result so far: 7501.137
If we subtract 5362 from 5420, we get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Advancing to step 11:
766 can be fit into 580 0 times, resulting in a remainder of 580.
Record the quotient 0 as the next digit in the result. 
Result so far: 7501.137
Subtract 0 from 580 to get 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5800, and continue the process.

Step 12:
766 goes into 5800 7 times with a remainder of 438.
The next digit of our result is 7. 
Result so far: 7501.13707
Subtract 5362 from 5800 to get 438.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4380, and continue the process.

Let's proceed to step 13:
If we divide 4380 by 766, we get 5 and a remainder of 550.
Put 5 as the next digit of the answer. 
Result so far: 7501.137075
Subtracting 3830 from 4380 leaves us with 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5500, and continue the process.

Step 14:
5500 divided by 766 is 7 with a remainder of 138.
Write down 7 as next digit of the result. 
Result so far: 7501.1370757
The remainder is 138 after subtracting 5362 from 5500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1380, and continue the process.

Moving on to step 15:
766 can be fit into 1380 1 times, resulting in a remainder of 614.
Use 1 as the next digit of our solution. 
Result so far: 7501.13707571
Deduct 766 from 1380 and we're left with 614.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6140, and continue the process.

The quotient of the division is 7501.13707571, and the remainder is 6.14e-07.