We look at the division of 14344 by 45 
We want to divide 14344 by 45.

Going ahead to step 1:
When dividing 1 by 45, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 45

Advancing to step 2:
45 goes into 14 0 times with a remainder of 14.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 14 and we're left with 14.
Grab the next digit (3) from the dividend, add it to 14, then carry on: 143 / 45

Let's proceed to step 3:
If we divide 143 by 45, we get 3 and a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we take 135 away from 143, we end up with 8.
Append the next digit (4) from the dividend to 8 and continue with: 84 / 45

Advancing to step 4:
When dividing 84 by 45, we get 1 with a remainder of 39.
Put 1 as the next digit of the answer. 
Result so far: 31.0
The remainder is 39 after subtracting 45 from 84.
Include the next digit (4) from the dividend after 39, then repeat: 394 / 45

On to step 5:
45 can be fit into 394 8 times, resulting in a remainder of 34.
The number 8 becomes the next digit in our result. 
Result so far: 318.0
If we take 360 away from 394, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 6:
340 divided by 45 is 7 with a remainder of 25.
The number 7 becomes the next digit in our result. 
Result so far: 318.7
If we subtract 315 from 340, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 7:
45 can be fit into 250 5 times, resulting in a remainder of 25.
The next digit of our result is 5. 
Result so far: 318.75
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
If we divide 250 by 45, we get 5 and a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 318.755
If we subtract 225 from 250, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 318.755, and the remainder is 0.0025.