389641 ÷ 63 
Our goal is to divide 389641 by 63.

Moving on to step 1:
63 goes into 3 0 times with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Include the next digit (8) from the dividend after 3, then repeat: 38 / 63

Let's proceed to step 2:
If we divide 38 by 63, we get 0 and a remainder of 38.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 38, we get 38.
Bring next digit (9) of the dividend behind the 38 and repeat the process: 389 / 63

Advancing to step 3:
When dividing 389 by 63, we get 6 with a remainder of 11.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we subtract 378 from 389, we get 11.
Include the next digit (6) from the dividend after 11, then repeat: 116 / 63

Moving on to step 4:
When dividing 116 by 63, we get 1 with a remainder of 53.
Put 1 as the next digit of the answer. 
Result so far: 61.0
Deduct 63 from 116 and we're left with 53.
Include the next digit (4) from the dividend after 53, then repeat: 534 / 63

On to step 5:
63 can be fit into 534 8 times, resulting in a remainder of 30.
The next digit of our result is 8. 
Result so far: 618.0
If we take 504 away from 534, we end up with 30.
Bring next digit (1) of the dividend behind the 30 and repeat the process: 301 / 63

Let's proceed to step 6:
When dividing 301 by 63, we get 4 with a remainder of 49.
The number 4 becomes the next digit in our result. 
Result so far: 6184.0
Subtracting 252 from 301 leaves us with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Advancing to step 7:
63 goes into 490 7 times with a remainder of 49.
Use 7 as the next digit of our solution. 
Result so far: 6184.7
The remainder is 49 after subtracting 441 from 490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Step 8:
If we divide 490 by 63, we get 7 and a remainder of 49.
The number 7 becomes the next digit in our result. 
Result so far: 6184.77
The remainder is 49 after subtracting 441 from 490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

The quotient of the division is 6184.77, and the remainder is 0.049.