We look at the division of 643759 by 34 
We want to figure out the number of times 643759 can be divided by 34.

Moving on to step 1:
The number 34 fits into 6 0 times, leaving a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 34

On to step 2:
34 goes into 64 1 times with a remainder of 30.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 34 from 64 and we're left with 30.
Grab the next digit (3) from the dividend, add it to 30, then carry on: 303 / 34

Let's proceed to step 3:
303 divided by 34 is 8 with a remainder of 31.
The next digit of our result is 8. 
Result so far: 18.0
Subtracting 272 from 303 leaves us with 31.
Bring next digit (7) of the dividend behind the 31 and repeat the process: 317 / 34

Moving on to step 4:
If we divide 317 by 34, we get 9 and a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 189.0
If we subtract 306 from 317, we get 11.
Include the next digit (5) from the dividend after 11, then repeat: 115 / 34

Let's proceed to step 5:
The number 34 fits into 115 3 times, leaving a remainder of 13.
The next digit of our result is 3. 
Result so far: 1893.0
Deduct 102 from 115 and we're left with 13.
Grab the next digit (9) from the dividend, add it to 13, then carry on: 139 / 34

Going ahead to step 6:
139 divided by 34 is 4 with a remainder of 3.
The number 4 becomes the next digit in our result. 
Result so far: 18934.0
Deduct 136 from 139 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 7:
34 goes into 30 0 times with a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 18934.0
The remainder is 30 after subtracting 0 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
When dividing 300 by 34, we get 8 with a remainder of 28.
The number 8 becomes the next digit in our result. 
Result so far: 18934.08
Subtract 272 from 300 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 9:
The number 34 fits into 280 8 times, leaving a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 18934.088
If we take 272 away from 280, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The final result is 18934.088 with a remainder of 0.0008.