Let's divide 155910 by 45
Our goal is to divide 155910 by 45.

On to step 1:
When dividing 1 by 45, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 45

On to step 2:
15 divided by 45 is 0 with a remainder of 15.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 15, we get 15.
Take the next digit (5) from the dividend and append it to 15, then repeat: 155 / 45

Going ahead to step 3:
45 goes into 155 3 times with a remainder of 20.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we take 135 away from 155, we end up with 20.
Append the next digit (9) from the dividend to 20 and continue with: 209 / 45

Let's proceed to step 4:
45 can be fit into 209 4 times, resulting in a remainder of 29.
Put 4 as the next digit of the answer. 
Result so far: 34.0
Subtract 180 from 209 to get 29.
Fetch the next digit (1) from the dividend, attach it to 29 and continue: 291 / 45

Moving on to step 5:
When dividing 291 by 45, we get 6 with a remainder of 21.
Record the quotient 6 as the next digit in the result. 
Result so far: 346.0
If we subtract 270 from 291, we get 21.
Bring next digit (0) of the dividend behind the 21 and repeat the process: 210 / 45

Going ahead to step 6:
The number 45 fits into 210 4 times, leaving a remainder of 30.
Write down 4 as next digit of the result. 
Result so far: 3464.0
The remainder is 30 after subtracting 180 from 210.
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 7:
45 goes into 300 6 times with a remainder of 30.
The next digit of our result is 6. 
Result so far: 3464.6
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:
300 divided by 45 is 6 with a remainder of 30.
Use 6 as the next digit of our solution. 
Result so far: 3464.66
Deduct 270 from 300 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.

The quotient of the division is 3464.66, and the remainder is 0.03.