We look at the division of 668742 by 45 
We want to figure out the number of times 668742 can be divided by 45.

Step 1:
The number 45 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 45

Moving on to step 2:
If we divide 66 by 45, we get 1 and a remainder of 21.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 45 from 66 leaves us with 21.
Bring next digit (8) of the dividend behind the 21 and repeat the process: 218 / 45

On to step 3:
If we divide 218 by 45, we get 4 and a remainder of 38.
Use 4 as the next digit of our solution. 
Result so far: 14.0
Deduct 180 from 218 and we're left with 38.
Bring next digit (7) of the dividend behind the 38 and repeat the process: 387 / 45

Going ahead to step 4:
The number 45 fits into 387 8 times, leaving a remainder of 27.
Record the quotient 8 as the next digit in the result. 
Result so far: 148.0
The remainder is 27 after subtracting 360 from 387.
Take the next digit (4) from the dividend and append it to 27, then repeat: 274 / 45

Moving on to step 5:
The number 45 fits into 274 6 times, leaving a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 1486.0
The remainder is 4 after subtracting 270 from 274.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 45

Moving on to step 6:
45 can be fit into 42 0 times, resulting in a remainder of 42.
The next digit of our result is 0. 
Result so far: 14860.0
If we take 0 away from 42, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 7:
45 can be fit into 420 9 times, resulting in a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 14860.9
Subtracting 405 from 420 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 8:
If we divide 150 by 45, we get 3 and a remainder of 15.
Put 3 as the next digit of the answer. 
Result so far: 14860.93
If we subtract 135 from 150, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 9:
When dividing 150 by 45, we get 3 with a remainder of 15.
The next digit of our result is 3. 
Result so far: 14860.933
Subtract 135 from 150 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Our division results in 14860.933 with a remaining 0.0015.