We're dividing 777697 by 71 
We want to figure out the number of times 777697 can be divided by 71.

Moving on to step 1:
When dividing 7 by 71, we get 0 with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 71

Moving on to step 2:
If we divide 77 by 71, we get 1 and a remainder of 6.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 71 from 77, we get 6.
Fetch the next digit (7) from the dividend, attach it to 6 and continue: 67 / 71

Step 3:
If we divide 67 by 71, we get 0 and a remainder of 67.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 67 after subtracting 0 from 67.
Grab the next digit (6) from the dividend, add it to 67, then carry on: 676 / 71

Step 4:
The number 71 fits into 676 9 times, leaving a remainder of 37.
Use 9 as the next digit of our solution. 
Result so far: 109.0
Subtracting 639 from 676 leaves us with 37.
Grab the next digit (9) from the dividend, add it to 37, then carry on: 379 / 71

On to step 5:
379 divided by 71 is 5 with a remainder of 24.
The number 5 becomes the next digit in our result. 
Result so far: 1095.0
If we subtract 355 from 379, we get 24.
Bring next digit (7) of the dividend behind the 24 and repeat the process: 247 / 71

Moving on to step 6:
If we divide 247 by 71, we get 3 and a remainder of 34.
The number 3 becomes the next digit in our result. 
Result so far: 10953.0
Subtracting 213 from 247 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 7:
340 divided by 71 is 4 with a remainder of 56.
Record the quotient 4 as the next digit in the result. 
Result so far: 10953.4
Subtracting 284 from 340 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Step 8:
560 divided by 71 is 7 with a remainder of 63.
Put 7 as the next digit of the answer. 
Result so far: 10953.47
If we subtract 497 from 560, we get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Moving on to step 9:
When dividing 630 by 71, we get 8 with a remainder of 62.
Use 8 as the next digit of our solution. 
Result so far: 10953.478
The remainder is 62 after subtracting 568 from 630.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 10:
71 goes into 620 8 times with a remainder of 52.
Put 8 as the next digit of the answer. 
Result so far: 10953.4788
Deduct 568 from 620 and we're left with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

The final outcome is 10953.4788, with a leftover of 0.00052.