We look at the division of 388778 by 638 
We want to figure out the number of times 388778 can be divided by 638.

Going ahead to step 1:
When dividing 3 by 638, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 638

Moving on to step 2:
38 divided by 638 is 0 with a remainder of 38.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 38 after subtracting 0 from 38.
Include the next digit (8) from the dividend after 38, then repeat: 388 / 638

Moving on to step 3:
When dividing 388 by 638, we get 0 with a remainder of 388.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 388 and we're left with 388.
Grab the next digit (7) from the dividend, add it to 388, then carry on: 3887 / 638

Advancing to step 4:
If we divide 3887 by 638, we get 6 and a remainder of 59.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we subtract 3828 from 3887, we get 59.
Fetch the next digit (7) from the dividend, attach it to 59 and continue: 597 / 638

Advancing to step 5:
597 divided by 638 is 0 with a remainder of 597.
The number 0 becomes the next digit in our result. 
Result so far: 60.0
Deduct 0 from 597 and we're left with 597.
Bring next digit (8) of the dividend behind the 597 and repeat the process: 5978 / 638

On to step 6:
638 can be fit into 5978 9 times, resulting in a remainder of 236.
Use 9 as the next digit of our solution. 
Result so far: 609.0
Deduct 5742 from 5978 and we're left with 236.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2360, and continue the process.

Going ahead to step 7:
2360 divided by 638 is 3 with a remainder of 446.
The number 3 becomes the next digit in our result. 
Result so far: 609.3
Subtract 1914 from 2360 to get 446.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4460, and continue the process.

Moving on to step 8:
When dividing 4460 by 638, we get 6 with a remainder of 632.
Write down 6 as next digit of the result. 
Result so far: 609.36
If we take 3828 away from 4460, we end up with 632.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6320, and continue the process.

Let's proceed to step 9:
638 can be fit into 6320 9 times, resulting in a remainder of 578.
The next digit of our result is 9. 
Result so far: 609.369
Subtracting 5742 from 6320 leaves us with 578.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5780, and continue the process.

Let's proceed to step 10:
When dividing 5780 by 638, we get 9 with a remainder of 38.
Use 9 as the next digit of our solution. 
Result so far: 609.3699
Deduct 5742 from 5780 and we're left with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The quotient of the division is 609.3699, and the remainder is 0.00038.