71755 ÷ 90 
We want to figure out the number of times 71755 can be divided by 90.

Advancing to step 1:
When dividing 7 by 90, we get 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 90

On to step 2:
90 can be fit into 71 0 times, resulting in a remainder of 71.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 71, we get 71.
Take the next digit (7) from the dividend and append it to 71, then repeat: 717 / 90

Going ahead to step 3:
90 goes into 717 7 times with a remainder of 87.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Deduct 630 from 717 and we're left with 87.
Bring next digit (5) of the dividend behind the 87 and repeat the process: 875 / 90

Step 4:
The number 90 fits into 875 9 times, leaving a remainder of 65.
Put 9 as the next digit of the answer. 
Result so far: 79.0
Subtract 810 from 875 to get 65.
Grab the next digit (5) from the dividend, add it to 65, then carry on: 655 / 90

Step 5:
655 divided by 90 is 7 with a remainder of 25.
The number 7 becomes the next digit in our result. 
Result so far: 797.0
Subtracting 630 from 655 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 6:
If we divide 250 by 90, we get 2 and a remainder of 70.
Record the quotient 2 as the next digit in the result. 
Result so far: 797.2
If we subtract 180 from 250, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 7:
90 can be fit into 700 7 times, resulting in a remainder of 70.
Use 7 as the next digit of our solution. 
Result so far: 797.27
Subtracting 630 from 700 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 8:
When dividing 700 by 90, we get 7 with a remainder of 70.
The number 7 becomes the next digit in our result. 
Result so far: 797.277
If we take 630 away from 700, we end up with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

The final outcome is 797.277, with a leftover of 0.007.