We're dividing 558379 by 86 
We're looking to find how many times 86 goes into 558379.

Going ahead to step 1:
86 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 86

On to step 2:
If we divide 55 by 86, we get 0 and a remainder of 55.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Bring next digit (8) of the dividend behind the 55 and repeat the process: 558 / 86

Advancing to step 3:
86 goes into 558 6 times with a remainder of 42.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Subtracting 516 from 558 leaves us with 42.
Include the next digit (3) from the dividend after 42, then repeat: 423 / 86

Moving on to step 4:
86 goes into 423 4 times with a remainder of 79.
Record the quotient 4 as the next digit in the result. 
Result so far: 64.0
Deduct 344 from 423 and we're left with 79.
Take the next digit (7) from the dividend and append it to 79, then repeat: 797 / 86

Let's proceed to step 5:
86 can be fit into 797 9 times, resulting in a remainder of 23.
Use 9 as the next digit of our solution. 
Result so far: 649.0
If we subtract 774 from 797, we get 23.
Include the next digit (9) from the dividend after 23, then repeat: 239 / 86

Step 6:
If we divide 239 by 86, we get 2 and a remainder of 67.
The next digit of our result is 2. 
Result so far: 6492.0
If we subtract 172 from 239, we 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 7:
86 goes into 670 7 times with a remainder of 68.
Put 7 as the next digit of the answer. 
Result so far: 6492.7
The remainder is 68 after subtracting 602 from 670.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Moving on to step 8:
When dividing 680 by 86, we get 7 with a remainder of 78.
Record the quotient 7 as the next digit in the result. 
Result so far: 6492.77
If we subtract 602 from 680, we get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

The final result is 6492.77 with a remainder of 0.078.