We're dividing 617753 by 45 
We're looking to find how many times 45 goes into 617753.

Advancing to step 1:
45 can be fit into 6 0 times, resulting in a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (1) from the dividend and append it to 6, then repeat: 61 / 45

Moving on to step 2:
45 goes into 61 1 times with a remainder of 16.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 16 after subtracting 45 from 61.
Include the next digit (7) from the dividend after 16, then repeat: 167 / 45

Moving on to step 3:
The number 45 fits into 167 3 times, leaving a remainder of 32.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
Subtracting 135 from 167 leaves us with 32.
Fetch the next digit (7) from the dividend, attach it to 32 and continue: 327 / 45

Moving on to step 4:
When dividing 327 by 45, we get 7 with a remainder of 12.
The next digit of our result is 7. 
Result so far: 137.0
Subtracting 315 from 327 leaves us with 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 45

On to step 5:
When dividing 125 by 45, we get 2 with a remainder of 35.
Put 2 as the next digit of the answer. 
Result so far: 1372.0
If we subtract 90 from 125, we get 35.
Grab the next digit (3) from the dividend, add it to 35, then carry on: 353 / 45

Step 6:
45 can be fit into 353 7 times, resulting in a remainder of 38.
The number 7 becomes the next digit in our result. 
Result so far: 13727.0
The remainder is 38 after subtracting 315 from 353.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Let's proceed to step 7:
The number 45 fits into 380 8 times, leaving a remainder of 20.
Use 8 as the next digit of our solution. 
Result so far: 13727.8
Subtract 360 from 380 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
200 divided by 45 is 4 with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 13727.84
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
45 can be fit into 200 4 times, resulting in a remainder of 20.
Record the quotient 4 as the next digit in the result. 
Result so far: 13727.844
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 13727.844 and a remainder of 0.002.