We look at the division of 558623 by 77 
Our goal is to divide 558623 by 77.

Advancing to step 1:
The number 77 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 77

Step 2:
When dividing 55 by 77, we get 0 with a remainder of 55.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 55, we end up with 55.
Append the next digit (8) from the dividend to 55 and continue with: 558 / 77

Moving on to step 3:
77 goes into 558 7 times with a remainder of 19.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtracting 539 from 558 leaves us with 19.
Fetch the next digit (6) from the dividend, attach it to 19 and continue: 196 / 77

Moving on to step 4:
If we divide 196 by 77, we get 2 and a remainder of 42.
Use 2 as the next digit of our solution. 
Result so far: 72.0
Subtracting 154 from 196 leaves us with 42.
Fetch the next digit (2) from the dividend, attach it to 42 and continue: 422 / 77

Going ahead to step 5:
77 can be fit into 422 5 times, resulting in a remainder of 37.
The next digit of our result is 5. 
Result so far: 725.0
If we subtract 385 from 422, we get 37.
Take the next digit (3) from the dividend and append it to 37, then repeat: 373 / 77

Going ahead to step 6:
If we divide 373 by 77, we get 4 and a remainder of 65.
Put 4 as the next digit of the answer. 
Result so far: 7254.0
Deduct 308 from 373 and we're left with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Going ahead to step 7:
When dividing 650 by 77, we get 8 with a remainder of 34.
Record the quotient 8 as the next digit in the result. 
Result so far: 7254.8
Subtract 616 from 650 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 8:
77 goes into 340 4 times with a remainder of 32.
Use 4 as the next digit of our solution. 
Result so far: 7254.84
Subtracting 308 from 340 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 9:
77 can be fit into 320 4 times, resulting in a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 7254.844
If we take 308 away from 320, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 7254.844 with a remainder of 0.0012.