We're dividing 386678 by 45 
We want to figure out the number of times 386678 can be divided by 45.

Going ahead to step 1:
When dividing 3 by 45, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (8) from the dividend to 3 and continue with: 38 / 45

On to step 2:
45 goes into 38 0 times with a remainder of 38.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 38 after subtracting 0 from 38.
Grab the next digit (6) from the dividend, add it to 38, then carry on: 386 / 45

Step 3:
45 can be fit into 386 8 times, resulting in a remainder of 26.
Put 8 as the next digit of the answer. 
Result so far: 8.0
If we subtract 360 from 386, we get 26.
Include the next digit (6) from the dividend after 26, then repeat: 266 / 45

On to step 4:
When dividing 266 by 45, we get 5 with a remainder of 41.
Record the quotient 5 as the next digit in the result. 
Result so far: 85.0
Subtracting 225 from 266 leaves us with 41.
Append the next digit (7) from the dividend to 41 and continue with: 417 / 45

Moving on to step 5:
417 divided by 45 is 9 with a remainder of 12.
Put 9 as the next digit of the answer. 
Result so far: 859.0
Deduct 405 from 417 and we're left with 12.
Fetch the next digit (8) from the dividend, attach it to 12 and continue: 128 / 45

Let's proceed to step 6:
128 divided by 45 is 2 with a remainder of 38.
The number 2 becomes the next digit in our result. 
Result so far: 8592.0
Subtract 90 from 128 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

On to step 7:
The number 45 fits into 380 8 times, leaving a remainder of 20.
Use 8 as the next digit of our solution. 
Result so far: 8592.8
Subtract 360 from 380 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
The number 45 fits into 200 4 times, leaving a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 8592.84
Subtracting 180 from 200 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 9:
When dividing 200 by 45, we get 4 with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 8592.844
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 8592.844, and the remainder is 0.002.