We're dividing 553630 by 86 
We want to divide 553630 by 86.

Advancing to step 1:
86 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 86

Step 2:
If we divide 55 by 86, we get 0 and a remainder of 55.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 55 and we're left with 55.
Grab the next digit (3) from the dividend, add it to 55, then carry on: 553 / 86

Moving on to step 3:
86 goes into 553 6 times with a remainder of 37.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
The remainder is 37 after subtracting 516 from 553.
Fetch the next digit (6) from the dividend, attach it to 37 and continue: 376 / 86

Step 4:
The number 86 fits into 376 4 times, leaving a remainder of 32.
Write down 4 as next digit of the result. 
Result so far: 64.0
Subtracting 344 from 376 leaves us with 32.
Take the next digit (3) from the dividend and append it to 32, then repeat: 323 / 86

Advancing to step 5:
If we divide 323 by 86, we get 3 and a remainder of 65.
Use 3 as the next digit of our solution. 
Result so far: 643.0
If we take 258 away from 323, we end up with 65.
Take the next digit (0) from the dividend and append it to 65, then repeat: 650 / 86

Advancing to step 6:
If we divide 650 by 86, we get 7 and a remainder of 48.
The next digit of our result is 7. 
Result so far: 6437.0
Subtracting 602 from 650 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 7:
When dividing 480 by 86, we get 5 with a remainder of 50.
The number 5 becomes the next digit in our result. 
Result so far: 6437.5
If we take 430 away from 480, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 8:
The number 86 fits into 500 5 times, leaving a remainder of 70.
The next digit of our result is 5. 
Result so far: 6437.55
If we take 430 away from 500, we end up 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.

The final outcome is 6437.55, with a leftover of 0.07.