Let's divide 634765 by 45
Our goal is to divide 634765 by 45.

Going ahead to step 1:
When dividing 6 by 45, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 45

Moving on to step 2:
If we divide 63 by 45, we get 1 and a remainder of 18.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 45 from 63 leaves us with 18.
Take the next digit (4) from the dividend and append it to 18, then repeat: 184 / 45

Advancing to step 3:
When dividing 184 by 45, we get 4 with a remainder of 4.
The next digit of our result is 4. 
Result so far: 14.0
Deduct 180 from 184 and we're left with 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 45

Going ahead to step 4:
47 divided by 45 is 1 with a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 141.0
If we subtract 45 from 47, we get 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 45

On to step 5:
If we divide 26 by 45, we get 0 and a remainder of 26.
Write down 0 as next digit of the result. 
Result so far: 1410.0
Subtracting 0 from 26 leaves us with 26.
Take the next digit (5) from the dividend and append it to 26, then repeat: 265 / 45

Going ahead to step 6:
If we divide 265 by 45, we get 5 and a remainder of 40.
Record the quotient 5 as the next digit in the result. 
Result so far: 14105.0
Subtract 225 from 265 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 7:
45 can be fit into 400 8 times, resulting in a remainder of 40.
The number 8 becomes the next digit in our result. 
Result so far: 14105.8
If we take 360 away from 400, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 8:
The number 45 fits into 400 8 times, leaving a remainder of 40.
Put 8 as the next digit of the answer. 
Result so far: 14105.88
The remainder is 40 after subtracting 360 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

After the division, we end up with 14105.88 and a remainder of 0.04.