We look at the division of 583440 by 45 
Let's see how many times 45 fits into 583440.

Moving on to step 1:
45 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 45

Let's proceed to step 2:
45 goes into 58 1 times with a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 45 away from 58, we end up with 13.
Fetch the next digit (3) from the dividend, attach it to 13 and continue: 133 / 45

Advancing to step 3:
The number 45 fits into 133 2 times, leaving a remainder of 43.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we take 90 away from 133, we end up with 43.
Fetch the next digit (4) from the dividend, attach it to 43 and continue: 434 / 45

Step 4:
When dividing 434 by 45, we get 9 with a remainder of 29.
The number 9 becomes the next digit in our result. 
Result so far: 129.0
If we subtract 405 from 434, we get 29.
Append the next digit (4) from the dividend to 29 and continue with: 294 / 45

On to step 5:
45 can be fit into 294 6 times, resulting in a remainder of 24.
The next digit of our result is 6. 
Result so far: 1296.0
If we take 270 away from 294, we end up with 24.
Include the next digit (0) from the dividend after 24, then repeat: 240 / 45

Going ahead to step 6:
45 can be fit into 240 5 times, resulting in a remainder of 15.
The next digit of our result is 5. 
Result so far: 12965.0
The remainder is 15 after subtracting 225 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 7:
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: 12965.3
Subtract 135 from 150 to 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.

On to step 8:
If we divide 150 by 45, we get 3 and a remainder of 15.
Put 3 as the next digit of the answer. 
Result so far: 12965.33
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.

The quotient of the division is 12965.33, and the remainder is 0.015.