We look at the division of 586168 by 90 
Our goal is to divide 586168 by 90.

Going ahead to step 1:
90 goes into 5 0 times 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.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 90

Advancing to step 2:
90 can be fit into 58 0 times, resulting in a remainder of 58.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 58 and we're left with 58.
Fetch the next digit (6) from the dividend, attach it to 58 and continue: 586 / 90

Moving on to step 3:
If we divide 586 by 90, we get 6 and a remainder of 46.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 46 after subtracting 540 from 586.
Fetch the next digit (1) from the dividend, attach it to 46 and continue: 461 / 90

Moving on to step 4:
461 divided by 90 is 5 with a remainder of 11.
Write down 5 as next digit of the result. 
Result so far: 65.0
Subtracting 450 from 461 leaves us with 11.
Take the next digit (6) from the dividend and append it to 11, then repeat: 116 / 90

Going ahead to step 5:
90 goes into 116 1 times with a remainder of 26.
Put 1 as the next digit of the answer. 
Result so far: 651.0
The remainder is 26 after subtracting 90 from 116.
Take the next digit (8) from the dividend and append it to 26, then repeat: 268 / 90

Let's proceed to step 6:
If we divide 268 by 90, we get 2 and a remainder of 88.
Record the quotient 2 as the next digit in the result. 
Result so far: 6512.0
Deduct 180 from 268 and we're left with 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 880, and continue the process.

Going ahead to step 7:
The number 90 fits into 880 9 times, leaving a remainder of 70.
The number 9 becomes the next digit in our result. 
Result so far: 6512.9
Subtract 810 from 880 to 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.

Moving on to step 8:
When dividing 700 by 90, we get 7 with a remainder of 70.
Use 7 as the next digit of our solution. 
Result so far: 6512.97
Deduct 630 from 700 and we're left 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.

Step 9:
The number 90 fits into 700 7 times, leaving a remainder of 70.
Use 7 as the next digit of our solution. 
Result so far: 6512.977
Subtract 630 from 700 to 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.

The final result is 6512.977 with a remainder of 0.007.