We look at the division of 586128 by 87 
We want to divide 586128 by 87.

Step 1:
5 divided by 87 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 87

Going ahead to step 2:
58 divided by 87 is 0 with a remainder of 58.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 58 after subtracting 0 from 58.
Bring next digit (6) of the dividend behind the 58 and repeat the process: 586 / 87

Step 3:
87 goes into 586 6 times with a remainder of 64.
The next digit of our result is 6. 
Result so far: 6.0
Deduct 522 from 586 and we're left with 64.
Grab the next digit (1) from the dividend, add it to 64, then carry on: 641 / 87

On to step 4:
The number 87 fits into 641 7 times, leaving a remainder of 32.
Write down 7 as next digit of the result. 
Result so far: 67.0
If we take 609 away from 641, we end up with 32.
Append the next digit (2) from the dividend to 32 and continue with: 322 / 87

On to step 5:
When dividing 322 by 87, we get 3 with a remainder of 61.
Write down 3 as next digit of the result. 
Result so far: 673.0
If we subtract 261 from 322, we get 61.
Bring next digit (8) of the dividend behind the 61 and repeat the process: 618 / 87

Advancing to step 6:
If we divide 618 by 87, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 6737.0
If we subtract 609 from 618, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
87 can be fit into 90 1 times, resulting in a remainder of 3.
The next digit of our result is 1. 
Result so far: 6737.1
If we take 87 away from 90, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 8:
The number 87 fits into 30 0 times, leaving a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 6737.1
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 9:
87 goes into 300 3 times with a remainder of 39.
Write down 3 as next digit of the result. 
Result so far: 6737.103
If we subtract 261 from 300, we get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 10:
The number 87 fits into 390 4 times, leaving a remainder of 42.
Write down 4 as next digit of the result. 
Result so far: 6737.1034
Subtract 348 from 390 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 11:
87 goes into 420 4 times with a remainder of 72.
The next digit of our result is 4. 
Result so far: 6737.10344
Deduct 348 from 420 and we're left with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

The final outcome is 6737.10344, with a leftover of 7.2e-05.