We look at the division of 312638 by 45 
We want to figure out the number of times 312638 can be divided by 45.

Let's proceed to step 1:
The number 45 fits into 3 0 times, leaving a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 45

Going ahead to step 2:
45 can be fit into 31 0 times, resulting in a remainder of 31.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 31, we end up with 31.
Bring next digit (2) of the dividend behind the 31 and repeat the process: 312 / 45

Advancing to step 3:
312 divided by 45 is 6 with a remainder of 42.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtracting 270 from 312 leaves us with 42.
Take the next digit (6) from the dividend and append it to 42, then repeat: 426 / 45

Let's proceed to step 4:
426 divided by 45 is 9 with a remainder of 21.
Write down 9 as next digit of the result. 
Result so far: 69.0
The remainder is 21 after subtracting 405 from 426.
Include the next digit (3) from the dividend after 21, then repeat: 213 / 45

On to step 5:
When dividing 213 by 45, we get 4 with a remainder of 33.
Write down 4 as next digit of the result. 
Result so far: 694.0
Subtracting 180 from 213 leaves us with 33.
Bring next digit (8) of the dividend behind the 33 and repeat the process: 338 / 45

Going ahead to step 6:
The number 45 fits into 338 7 times, leaving a remainder of 23.
The next digit of our result is 7. 
Result so far: 6947.0
The remainder is 23 after subtracting 315 from 338.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

On to step 7:
45 can be fit into 230 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 6947.5
If we subtract 225 from 230, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 8:
45 can be fit into 50 1 times, resulting in a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 6947.51
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 9:
45 goes into 50 1 times with a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 6947.511
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Our division results in 6947.511 with a remaining 0.0005.