We look at the division of 565105 by 87 
Our goal is to divide 565105 by 87.

Step 1:
When dividing 5 by 87, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 87

Advancing to step 2:
56 divided by 87 is 0 with a remainder of 56.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 56 after subtracting 0 from 56.
Fetch the next digit (5) from the dividend, attach it to 56 and continue: 565 / 87

Advancing to step 3:
When dividing 565 by 87, we get 6 with a remainder of 43.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we take 522 away from 565, we end up with 43.
Include the next digit (1) from the dividend after 43, then repeat: 431 / 87

Let's proceed to step 4:
The number 87 fits into 431 4 times, leaving a remainder of 83.
Write down 4 as next digit of the result. 
Result so far: 64.0
If we subtract 348 from 431, we get 83.
Fetch the next digit (0) from the dividend, attach it to 83 and continue: 830 / 87

Going ahead to step 5:
When dividing 830 by 87, we get 9 with a remainder of 47.
Record the quotient 9 as the next digit in the result. 
Result so far: 649.0
Subtracting 783 from 830 leaves us with 47.
Fetch the next digit (5) from the dividend, attach it to 47 and continue: 475 / 87

On to step 6:
If we divide 475 by 87, we get 5 and a remainder of 40.
Record the quotient 5 as the next digit in the result. 
Result so far: 6495.0
If we subtract 435 from 475, 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.

Moving on to step 7:
If we divide 400 by 87, we get 4 and a remainder of 52.
Record the quotient 4 as the next digit in the result. 
Result so far: 6495.4
If we subtract 348 from 400, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Advancing to step 8:
The number 87 fits into 520 5 times, leaving a remainder of 85.
Record the quotient 5 as the next digit in the result. 
Result so far: 6495.45
The remainder is 85 after subtracting 435 from 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 850, and continue the process.

Moving on to step 9:
850 divided by 87 is 9 with a remainder of 67.
Put 9 as the next digit of the answer. 
Result so far: 6495.459
Subtract 783 from 850 to get 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Let's proceed to step 10:
87 goes into 670 7 times with a remainder of 61.
The next digit of our result is 7. 
Result so far: 6495.4597
Deduct 609 from 670 and we're left with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Going ahead to step 11:
When dividing 610 by 87, we get 7 with a remainder of 1.
The next digit of our result is 7. 
Result so far: 6495.45977
The remainder is 1 after subtracting 609 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 6495.45977 with a balance of 1e-06.