We look at the division of 584260 by 45 
We're looking to find how many times 45 goes into 584260.

Going ahead to step 1:
45 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
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 / 45

Step 2:
45 can be fit into 58 1 times, resulting in a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 45 from 58 to get 13.
Append the next digit (4) from the dividend to 13 and continue with: 134 / 45

On to step 3:
45 goes into 134 2 times with a remainder of 44.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
If we subtract 90 from 134, we get 44.
Append the next digit (2) from the dividend to 44 and continue with: 442 / 45

Moving on to step 4:
45 can be fit into 442 9 times, resulting in a remainder of 37.
Put 9 as the next digit of the answer. 
Result so far: 129.0
If we take 405 away from 442, we end up with 37.
Bring next digit (6) of the dividend behind the 37 and repeat the process: 376 / 45

On to step 5:
If we divide 376 by 45, we get 8 and a remainder of 16.
The next digit of our result is 8. 
Result so far: 1298.0
If we take 360 away from 376, we end up with 16.
Append the next digit (0) from the dividend to 16 and continue with: 160 / 45

Moving on to step 6:
45 goes into 160 3 times with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 12983.0
Subtracting 135 from 160 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 7:
The number 45 fits into 250 5 times, leaving a remainder of 25.
The next digit of our result is 5. 
Result so far: 12983.5
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 8:
The number 45 fits into 250 5 times, leaving a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 12983.55
Subtracting 225 from 250 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 12983.55 with a balance of 0.025.