We're dividing 586564 by 86 
We want to figure out the number of times 586564 can be divided by 86.

Let's proceed to step 1:
86 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 86

Going ahead to step 2:
86 can be fit into 58 0 times, resulting in 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.
Include the next digit (6) from the dividend after 58, then repeat: 586 / 86

Going ahead to step 3:
If we divide 586 by 86, we get 6 and a remainder of 70.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
The remainder is 70 after subtracting 516 from 586.
Fetch the next digit (5) from the dividend, attach it to 70 and continue: 705 / 86

Moving on to step 4:
When dividing 705 by 86, we get 8 with a remainder of 17.
The number 8 becomes the next digit in our result. 
Result so far: 68.0
If we subtract 688 from 705, we get 17.
Take the next digit (6) from the dividend and append it to 17, then repeat: 176 / 86

Going ahead to step 5:
When dividing 176 by 86, we get 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 682.0
The remainder is 4 after subtracting 172 from 176.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 86

On to step 6:
The number 86 fits into 44 0 times, leaving a remainder of 44.
Use 0 as the next digit of our solution. 
Result so far: 6820.0
The remainder is 44 after subtracting 0 from 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Going ahead to step 7:
The number 86 fits into 440 5 times, leaving a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 6820.5
Subtract 430 from 440 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 8:
86 can be fit into 100 1 times, resulting in a remainder of 14.
The next digit of our result is 1. 
Result so far: 6820.51
Subtracting 86 from 100 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 9:
86 goes into 140 1 times with a remainder of 54.
Use 1 as the next digit of our solution. 
Result so far: 6820.511
The remainder is 54 after subtracting 86 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

The final result is 6820.511 with a remainder of 0.0054.