We're dividing 766589 by 71 
We want to figure out the number of times 766589 can be divided by 71.

Advancing to step 1:
The number 71 fits into 7 0 times, leaving a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 71

Step 2:
The number 71 fits into 76 1 times, leaving a remainder of 5.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 5 after subtracting 71 from 76.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 71

Going ahead to step 3:
71 goes into 56 0 times with a remainder of 56.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Deduct 0 from 56 and we're left with 56.
Fetch the next digit (5) from the dividend, attach it to 56 and continue: 565 / 71

Going ahead to step 4:
71 goes into 565 7 times with a remainder of 68.
Record the quotient 7 as the next digit in the result. 
Result so far: 107.0
Deduct 497 from 565 and we're left with 68.
Fetch the next digit (8) from the dividend, attach it to 68 and continue: 688 / 71

Going ahead to step 5:
When dividing 688 by 71, we get 9 with a remainder of 49.
Write down 9 as next digit of the result. 
Result so far: 1079.0
The remainder is 49 after subtracting 639 from 688.
Bring next digit (9) of the dividend behind the 49 and repeat the process: 499 / 71

Moving on to step 6:
If we divide 499 by 71, we get 7 and a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 10797.0
The remainder is 2 after subtracting 497 from 499.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
71 goes into 20 0 times with a remainder of 20.
The next digit of our result is 0. 
Result so far: 10797.0
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
200 divided by 71 is 2 with a remainder of 58.
The number 2 becomes the next digit in our result. 
Result so far: 10797.02
If we subtract 142 from 200, 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.

Step 9:
580 divided by 71 is 8 with a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 10797.028
If we take 568 away from 580, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 10:
71 can be fit into 120 1 times, resulting in a remainder of 49.
Record the quotient 1 as the next digit in the result. 
Result so far: 10797.0281
The remainder is 49 after subtracting 71 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Moving on to step 11:
The number 71 fits into 490 6 times, leaving a remainder of 64.
Use 6 as the next digit of our solution. 
Result so far: 10797.02816
If we subtract 426 from 490, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Going ahead to step 12:
71 can be fit into 640 9 times, resulting in a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 10797.028169
Subtract 639 from 640 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 13:
The number 71 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 10797.028169
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 14:
The number 71 fits into 100 1 times, leaving a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 10797.02816901
If we subtract 71 from 100, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

The final result is 10797.02816901 with a remainder of 2.9e-08.