We look at the division of 871177 by 90 
We want to figure out the number of times 871177 can be divided by 90.

Advancing to step 1:
8 divided by 90 is 0 with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Bring next digit (7) of the dividend behind the 8 and repeat the process: 87 / 90

Step 2:
90 can be fit into 87 0 times, resulting in a remainder of 87.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 87 after subtracting 0 from 87.
Bring next digit (1) of the dividend behind the 87 and repeat the process: 871 / 90

Step 3:
90 goes into 871 9 times with a remainder of 61.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
Subtract 810 from 871 to get 61.
Bring next digit (1) of the dividend behind the 61 and repeat the process: 611 / 90

On to step 4:
611 divided by 90 is 6 with a remainder of 71.
The number 6 becomes the next digit in our result. 
Result so far: 96.0
Subtracting 540 from 611 leaves us with 71.
Include the next digit (7) from the dividend after 71, then repeat: 717 / 90

Let's proceed to step 5:
The number 90 fits into 717 7 times, leaving a remainder of 87.
Write down 7 as next digit of the result. 
Result so far: 967.0
Subtract 630 from 717 to get 87.
Include the next digit (7) from the dividend after 87, then repeat: 877 / 90

Going ahead to step 6:
90 can be fit into 877 9 times, resulting in a remainder of 67.
Put 9 as the next digit of the answer. 
Result so far: 9679.0
Deduct 810 from 877 and we're left with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 7:
When dividing 670 by 90, we get 7 with a remainder of 40.
Put 7 as the next digit of the answer. 
Result so far: 9679.7
If we subtract 630 from 670, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 8:
The number 90 fits into 400 4 times, leaving a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 9679.74
If we take 360 away from 400, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 9:
90 can be fit into 400 4 times, resulting in a remainder of 40.
Use 4 as the next digit of our solution. 
Result so far: 9679.744
Subtract 360 from 400 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The quotient of the division is 9679.744, and the remainder is 0.004.