We're dividing 344644 by 35 
We're looking to find how many times 35 goes into 344644.

Going ahead to step 1:
35 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 35

Advancing to step 2:
The number 35 fits into 34 0 times, leaving a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 34 and we're left with 34.
Bring next digit (4) of the dividend behind the 34 and repeat the process: 344 / 35

Step 3:
When dividing 344 by 35, we get 9 with a remainder of 29.
The next digit of our result is 9. 
Result so far: 9.0
If we subtract 315 from 344, we get 29.
Grab the next digit (6) from the dividend, add it to 29, then carry on: 296 / 35

Step 4:
When dividing 296 by 35, we get 8 with a remainder of 16.
Write down 8 as next digit of the result. 
Result so far: 98.0
If we subtract 280 from 296, we get 16.
Grab the next digit (4) from the dividend, add it to 16, then carry on: 164 / 35

Moving on to step 5:
If we divide 164 by 35, we get 4 and a remainder of 24.
Put 4 as the next digit of the answer. 
Result so far: 984.0
If we take 140 away from 164, we end up with 24.
Include the next digit (4) from the dividend after 24, then repeat: 244 / 35

Step 6:
35 goes into 244 6 times with a remainder of 34.
The next digit of our result is 6. 
Result so far: 9846.0
Deduct 210 from 244 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 7:
The number 35 fits into 340 9 times, leaving a remainder of 25.
The number 9 becomes the next digit in our result. 
Result so far: 9846.9
Deduct 315 from 340 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 8:
If we divide 250 by 35, we get 7 and a remainder of 5.
Record the quotient 7 as the next digit in the result. 
Result so far: 9846.97
Subtract 245 from 250 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 9:
When dividing 50 by 35, we get 1 with a remainder of 15.
The number 1 becomes the next digit in our result. 
Result so far: 9846.971
The remainder is 15 after subtracting 35 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 10:
If we divide 150 by 35, we get 4 and a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 9846.9714
Deduct 140 from 150 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 11:
If we divide 100 by 35, we get 2 and a remainder of 30.
Put 2 as the next digit of the answer. 
Result so far: 9846.97142
Subtracting 70 from 100 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 12:
When dividing 300 by 35, we get 8 with a remainder of 20.
The next digit of our result is 8. 
Result so far: 9846.971428
Subtract 280 from 300 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 13:
200 divided by 35 is 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 9846.9714285
Deduct 175 from 200 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 14:
35 goes into 250 7 times with a remainder of 5.
Record the quotient 7 as the next digit in the result. 
Result so far: 9846.97142857
If we subtract 245 from 250, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final outcome is 9846.97142857, with a leftover of 5e-09.