We're dividing 587593 by 79 
Our goal is to divide 587593 by 79.

On to step 1:
The number 79 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 79

On to step 2:
58 divided by 79 is 0 with a remainder of 58.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 58, we get 58.
Bring next digit (7) of the dividend behind the 58 and repeat the process: 587 / 79

On to step 3:
587 divided by 79 is 7 with a remainder of 34.
The next digit of our result is 7. 
Result so far: 7.0
If we take 553 away from 587, we end up with 34.
Take the next digit (5) from the dividend and append it to 34, then repeat: 345 / 79

On to step 4:
79 can be fit into 345 4 times, resulting in a remainder of 29.
Write down 4 as next digit of the result. 
Result so far: 74.0
The remainder is 29 after subtracting 316 from 345.
Fetch the next digit (9) from the dividend, attach it to 29 and continue: 299 / 79

Going ahead to step 5:
79 can be fit into 299 3 times, resulting in a remainder of 62.
The next digit of our result is 3. 
Result so far: 743.0
If we subtract 237 from 299, we get 62.
Take the next digit (3) from the dividend and append it to 62, then repeat: 623 / 79

Let's proceed to step 6:
79 can be fit into 623 7 times, resulting in a remainder of 70.
Write down 7 as next digit of the result. 
Result so far: 7437.0
If we subtract 553 from 623, we 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 7:
The number 79 fits into 700 8 times, leaving a remainder of 68.
The next digit of our result is 8. 
Result so far: 7437.8
Deduct 632 from 700 and we're left with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

On to step 8:
680 divided by 79 is 8 with a remainder of 48.
The number 8 becomes the next digit in our result. 
Result so far: 7437.88
Deduct 632 from 680 and we're left 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.

The final outcome is 7437.88, with a leftover of 0.048.