We're dividing 586353 by 45 
We want to figure out the number of times 586353 can be divided by 45.

Step 1:
The number 45 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 45

Going ahead to step 2:
45 can be fit into 58 1 times, resulting in a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 13 after subtracting 45 from 58.
Append the next digit (6) from the dividend to 13 and continue with: 136 / 45

Step 3:
45 goes into 136 3 times with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtract 135 from 136 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 45

Going ahead to step 4:
45 can be fit into 13 0 times, resulting in a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 130.0
If we subtract 0 from 13, we get 13.
Take the next digit (5) from the dividend and append it to 13, then repeat: 135 / 45

Going ahead to step 5:
When dividing 135 by 45, we get 3 with a remainder of 0.
The next digit of our result is 3. 
Result so far: 1303.0
Subtract 135 from 135 to get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 45

Moving on to step 6:
When dividing 3 by 45, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 13030.0
Subtract 0 from 3 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
When dividing 30 by 45, we get 0 with a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 13030.0
If we take 0 away from 30, 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.

Advancing to step 8:
300 divided by 45 is 6 with a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 13030.06
Subtracting 270 from 300 leaves us 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.

Let's proceed to step 9:
The number 45 fits into 300 6 times, leaving a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 13030.066
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.

The final outcome is 13030.066, with a leftover of 0.003.