We're dividing 312915 by 45 
We're looking to find how many times 45 goes into 312915.

Advancing to step 1:
3 divided by 45 is 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 45

Advancing to step 2:
When dividing 31 by 45, we get 0 with a remainder of 31.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 31, we get 31.
Fetch the next digit (2) from the dividend, attach it to 31 and continue: 312 / 45

Advancing to step 3:
The number 45 fits into 312 6 times, leaving a remainder of 42.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtracting 270 from 312 leaves us with 42.
Append the next digit (9) from the dividend to 42 and continue with: 429 / 45

Let's proceed to step 4:
When dividing 429 by 45, we get 9 with a remainder of 24.
Put 9 as the next digit of the answer. 
Result so far: 69.0
If we take 405 away from 429, we end up with 24.
Grab the next digit (1) from the dividend, add it to 24, then carry on: 241 / 45

Going ahead to step 5:
The number 45 fits into 241 5 times, leaving a remainder of 16.
Write down 5 as next digit of the result. 
Result so far: 695.0
If we take 225 away from 241, we end up with 16.
Grab the next digit (5) from the dividend, add it to 16, then carry on: 165 / 45

On to step 6:
165 divided by 45 is 3 with a remainder of 30.
Record the quotient 3 as the next digit in the result. 
Result so far: 6953.0
Subtract 135 from 165 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 7:
When dividing 300 by 45, we get 6 with a remainder of 30.
The next digit of our result is 6. 
Result so far: 6953.6
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.

Step 8:
45 can be fit into 300 6 times, resulting in a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 6953.66
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 6953.66, and the remainder is 0.03.