We're dividing 629535 by 45 
We want to figure out the number of times 629535 can be divided by 45.

Advancing to step 1:
45 can be fit into 6 0 times, resulting in a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Grab the next digit (2) from the dividend, add it to 6, then carry on: 62 / 45

On to step 2:
When dividing 62 by 45, we get 1 with a remainder of 17.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 45 away from 62, we end up with 17.
Fetch the next digit (9) from the dividend, attach it to 17 and continue: 179 / 45

Step 3:
When dividing 179 by 45, we get 3 with a remainder of 44.
Write down 3 as next digit of the result. 
Result so far: 13.0
Deduct 135 from 179 and we're left with 44.
Take the next digit (5) from the dividend and append it to 44, then repeat: 445 / 45

Step 4:
45 can be fit into 445 9 times, resulting in a remainder of 40.
Put 9 as the next digit of the answer. 
Result so far: 139.0
The remainder is 40 after subtracting 405 from 445.
Bring next digit (3) of the dividend behind the 40 and repeat the process: 403 / 45

Moving on to step 5:
403 divided by 45 is 8 with a remainder of 43.
Use 8 as the next digit of our solution. 
Result so far: 1398.0
The remainder is 43 after subtracting 360 from 403.
Bring next digit (5) of the dividend behind the 43 and repeat the process: 435 / 45

On to step 6:
The number 45 fits into 435 9 times, leaving a remainder of 30.
The number 9 becomes the next digit in our result. 
Result so far: 13989.0
Deduct 405 from 435 and we're left 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.

Step 7:
The number 45 fits into 300 6 times, leaving a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 13989.6
Subtract 270 from 300 to get 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 8:
45 goes into 300 6 times with a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 13989.66
If we subtract 270 from 300, we get 30.
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 result is 13989.66 with a remainder of 0.03.