3633587 divided by 643 
Our goal is to divide 3633587 by 643.

Step 1:
If we divide 3 by 643, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Include the next digit (6) from the dividend after 3, then repeat: 36 / 643

On to step 2:
643 can be fit into 36 0 times, resulting in a remainder of 36.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 36, we end up with 36.
Fetch the next digit (3) from the dividend, attach it to 36 and continue: 363 / 643

Advancing to step 3:
If we divide 363 by 643, we get 0 and a remainder of 363.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 363 and we're left with 363.
Fetch the next digit (3) from the dividend, attach it to 363 and continue: 3633 / 643

Moving on to step 4:
The number 643 fits into 3633 5 times, leaving a remainder of 418.
The next digit of our result is 5. 
Result so far: 5.0
If we take 3215 away from 3633, we end up with 418.
Append the next digit (5) from the dividend to 418 and continue with: 4185 / 643

Moving on to step 5:
643 can be fit into 4185 6 times, resulting in a remainder of 327.
The next digit of our result is 6. 
Result so far: 56.0
Deduct 3858 from 4185 and we're left with 327.
Include the next digit (8) from the dividend after 327, then repeat: 3278 / 643

Let's proceed to step 6:
3278 divided by 643 is 5 with a remainder of 63.
The next digit of our result is 5. 
Result so far: 565.0
The remainder is 63 after subtracting 3215 from 3278.
Bring next digit (7) of the dividend behind the 63 and repeat the process: 637 / 643

Moving on to step 7:
When dividing 637 by 643, we get 0 with a remainder of 637.
The number 0 becomes the next digit in our result. 
Result so far: 5650.0
If we take 0 away from 637, we end up with 637.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6370, and continue the process.

Going ahead to step 8:
643 goes into 6370 9 times with a remainder of 583.
Use 9 as the next digit of our solution. 
Result so far: 5650.9
Subtracting 5787 from 6370 leaves us with 583.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5830, and continue the process.

Step 9:
When dividing 5830 by 643, we get 9 with a remainder of 43.
Record the quotient 9 as the next digit in the result. 
Result so far: 5650.99
Subtract 5787 from 5830 to get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

The final result is 5650.99 with a remainder of 0.043.