582681 ÷ 45 
Let's see how many times 45 fits into 582681.

Let's proceed to step 1:
If we divide 5 by 45, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 45

Step 2:
45 can be fit into 58 1 times, resulting in 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.
Append the next digit (2) from the dividend to 13 and continue with: 132 / 45

Moving on to step 3:
The number 45 fits into 132 2 times, leaving a remainder of 42.
Write down 2 as next digit of the result. 
Result so far: 12.0
If we subtract 90 from 132, we get 42.
Append the next digit (6) from the dividend to 42 and continue with: 426 / 45

On to step 4:
When dividing 426 by 45, we get 9 with a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 129.0
If we take 405 away from 426, we end up with 21.
Fetch the next digit (8) from the dividend, attach it to 21 and continue: 218 / 45

Let's proceed to step 5:
The number 45 fits into 218 4 times, leaving a remainder of 38.
The number 4 becomes the next digit in our result. 
Result so far: 1294.0
Subtract 180 from 218 to get 38.
Grab the next digit (1) from the dividend, add it to 38, then carry on: 381 / 45

On to step 6:
The number 45 fits into 381 8 times, leaving a remainder of 21.
The next digit of our result is 8. 
Result so far: 12948.0
Subtracting 360 from 381 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
When dividing 210 by 45, we get 4 with a remainder of 30.
The number 4 becomes the next digit in our result. 
Result so far: 12948.4
If we take 180 away from 210, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
If we divide 300 by 45, we get 6 and a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 12948.46
Subtract 270 from 300 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 9:
45 can be fit into 300 6 times, resulting in a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 12948.466
The remainder is 30 after subtracting 270 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 12948.466 with a balance of 0.003.