We look at the division of 643771 by 34 
We want to figure out the number of times 643771 can be divided by 34.

Step 1:
34 can be fit into 6 0 times, resulting in a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 34

Advancing to step 2:
When dividing 64 by 34, we get 1 with a remainder of 30.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 34 from 64 leaves us with 30.
Include the next digit (3) from the dividend after 30, then repeat: 303 / 34

Step 3:
The number 34 fits into 303 8 times, leaving a remainder of 31.
The next digit of our result is 8. 
Result so far: 18.0
Deduct 272 from 303 and we're left with 31.
Include the next digit (7) from the dividend after 31, then repeat: 317 / 34

On to step 4:
When dividing 317 by 34, we get 9 with a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 189.0
The remainder is 11 after subtracting 306 from 317.
Append the next digit (7) from the dividend to 11 and continue with: 117 / 34

Advancing to step 5:
If we divide 117 by 34, we get 3 and a remainder of 15.
The next digit of our result is 3. 
Result so far: 1893.0
Deduct 102 from 117 and we're left with 15.
Bring next digit (1) of the dividend behind the 15 and repeat the process: 151 / 34

Let's proceed to step 6:
34 goes into 151 4 times with a remainder of 15.
The number 4 becomes the next digit in our result. 
Result so far: 18934.0
Subtract 136 from 151 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 7:
34 goes into 150 4 times with a remainder of 14.
The next digit of our result is 4. 
Result so far: 18934.4
Subtracting 136 from 150 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 8:
34 goes into 140 4 times with a remainder of 4.
The next digit of our result is 4. 
Result so far: 18934.44
The remainder is 4 after subtracting 136 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

After the division, we end up with 18934.44 and a remainder of 0.004.