We're dividing 457259 by 45 
We're looking to find how many times 45 goes into 457259.

Advancing to step 1:
45 goes into 4 0 times with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 45

On to step 2:
45 can be fit into 45 1 times, resulting in a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 0 after subtracting 45 from 45.
Include the next digit (7) from the dividend after 0, then repeat: 7 / 45

Advancing to step 3:
7 divided by 45 is 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 10.0
The remainder is 7 after subtracting 0 from 7.
Take the next digit (2) from the dividend and append it to 7, then repeat: 72 / 45

On to step 4:
45 can be fit into 72 1 times, resulting in a remainder of 27.
Put 1 as the next digit of the answer. 
Result so far: 101.0
If we subtract 45 from 72, we get 27.
Append the next digit (5) from the dividend to 27 and continue with: 275 / 45

Let's proceed to step 5:
If we divide 275 by 45, we get 6 and a remainder of 5.
Write down 6 as next digit of the result. 
Result so far: 1016.0
If we subtract 270 from 275, we get 5.
Include the next digit (9) from the dividend after 5, then repeat: 59 / 45

Advancing to step 6:
If we divide 59 by 45, we get 1 and a remainder of 14.
Put 1 as the next digit of the answer. 
Result so far: 10161.0
Subtract 45 from 59 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 7:
If we divide 140 by 45, we get 3 and a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 10161.3
If we take 135 away from 140, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 8:
When dividing 50 by 45, we get 1 with a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 10161.31
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 9:
45 can be fit into 50 1 times, resulting in a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 10161.311
If we take 45 away from 50, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final result is 10161.311 with a remainder of 0.0005.