Let's divide 588768 by 45
We're looking to find how many times 45 goes into 588768.

Moving on to step 1:
If we divide 5 by 45, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 45

On to step 2:
58 divided by 45 is 1 with a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 45 from 58 to get 13.
Grab the next digit (8) from the dividend, add it to 13, then carry on: 138 / 45

Let's proceed to step 3:
When dividing 138 by 45, we get 3 with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtract 135 from 138 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 45

On to step 4:
37 divided by 45 is 0 with a remainder of 37.
Write down 0 as next digit of the result. 
Result so far: 130.0
Deduct 0 from 37 and we're left with 37.
Bring next digit (6) of the dividend behind the 37 and repeat the process: 376 / 45

Going ahead to step 5:
376 divided by 45 is 8 with a remainder of 16.
Put 8 as the next digit of the answer. 
Result so far: 1308.0
If we take 360 away from 376, we end up with 16.
Take the next digit (8) from the dividend and append it to 16, then repeat: 168 / 45

Moving on to step 6:
The number 45 fits into 168 3 times, leaving a remainder of 33.
Record the quotient 3 as the next digit in the result. 
Result so far: 13083.0
If we take 135 away from 168, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Going ahead to step 7:
330 divided by 45 is 7 with a remainder of 15.
The number 7 becomes the next digit in our result. 
Result so far: 13083.7
If we take 315 away from 330, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 8:
45 can be fit into 150 3 times, resulting in a remainder of 15.
The number 3 becomes the next digit in our result. 
Result so far: 13083.73
If we subtract 135 from 150, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 9:
45 goes into 150 3 times with a remainder of 15.
Record the quotient 3 as the next digit in the result. 
Result so far: 13083.733
Deduct 135 from 150 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

In conclusion, the division gives 13083.733 with a balance of 0.0015.