We're dividing 643741 by 63 
Let's see how many times 63 fits into 643741.

Going ahead to step 1:
6 divided by 63 is 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (4) from the dividend after 6, then repeat: 64 / 63

Moving on to step 2:
64 divided by 63 is 1 with a remainder of 1.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 63 from 64, we get 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 63

Let's proceed to step 3:
If we divide 13 by 63, we get 0 and a remainder of 13.
Write down 0 as next digit of the result. 
Result so far: 10.0
Deduct 0 from 13 and we're left with 13.
Include the next digit (7) from the dividend after 13, then repeat: 137 / 63

Step 4:
63 goes into 137 2 times with a remainder of 11.
The number 2 becomes the next digit in our result. 
Result so far: 102.0
Subtracting 126 from 137 leaves us with 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 63

Going ahead to step 5:
63 can be fit into 114 1 times, resulting in a remainder of 51.
The next digit of our result is 1. 
Result so far: 1021.0
The remainder is 51 after subtracting 63 from 114.
Grab the next digit (1) from the dividend, add it to 51, then carry on: 511 / 63

On to step 6:
If we divide 511 by 63, we get 8 and a remainder of 7.
Put 8 as the next digit of the answer. 
Result so far: 10218.0
The remainder is 7 after subtracting 504 from 511.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
70 divided by 63 is 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 10218.1
The remainder is 7 after subtracting 63 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
When dividing 70 by 63, we get 1 with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 10218.11
Deduct 63 from 70 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

After the division, we end up with 10218.11 and a remainder of 0.007.