We're dividing 678351 by 45 
We're looking to find how many times 45 goes into 678351.

Advancing to step 1:
If we divide 6 by 45, we get 0 and a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (7) from the dividend, attach it to 6 and continue: 67 / 45

Going ahead to step 2:
45 can be fit into 67 1 times, resulting in a remainder of 22.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 22 after subtracting 45 from 67.
Grab the next digit (8) from the dividend, add it to 22, then carry on: 228 / 45

Going ahead to step 3:
When dividing 228 by 45, we get 5 with a remainder of 3.
Put 5 as the next digit of the answer. 
Result so far: 15.0
If we subtract 225 from 228, we get 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 45

Moving on to step 4:
When dividing 33 by 45, we get 0 with a remainder of 33.
The next digit of our result is 0. 
Result so far: 150.0
If we take 0 away from 33, we end up with 33.
Include the next digit (5) from the dividend after 33, then repeat: 335 / 45

Let's proceed to step 5:
45 can be fit into 335 7 times, resulting in a remainder of 20.
Record the quotient 7 as the next digit in the result. 
Result so far: 1507.0
Subtract 315 from 335 to get 20.
Bring next digit (1) of the dividend behind the 20 and repeat the process: 201 / 45

Step 6:
If we divide 201 by 45, we get 4 and a remainder of 21.
Use 4 as the next digit of our solution. 
Result so far: 15074.0
Subtracting 180 from 201 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
If we divide 210 by 45, we get 4 and a remainder of 30.
The next digit of our result is 4. 
Result so far: 15074.4
If we subtract 180 from 210, we 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.

Moving on to step 8:
45 can be fit into 300 6 times, resulting in a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 15074.46
If we subtract 270 from 300, we 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.

Going ahead to step 9:
If we divide 300 by 45, we get 6 and a remainder of 30.
Write down 6 as next digit of the result. 
Result so far: 15074.466
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.

The final result is 15074.466 with a remainder of 0.003.