We look at the division of 409684 by 35 
We want to figure out the number of times 409684 can be divided by 35.

Advancing to step 1:
If we divide 4 by 35, we get 0 and a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 35

On to step 2:
35 goes into 40 1 times with a remainder of 5.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 35 from 40 and we're left with 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 35

Advancing to step 3:
The number 35 fits into 59 1 times, leaving a remainder of 24.
The next digit of our result is 1. 
Result so far: 11.0
If we subtract 35 from 59, we get 24.
Append the next digit (6) from the dividend to 24 and continue with: 246 / 35

Let's proceed to step 4:
When dividing 246 by 35, we get 7 with a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 117.0
If we subtract 245 from 246, we get 1.
Take the next digit (8) from the dividend and append it to 1, then repeat: 18 / 35

Advancing to step 5:
The number 35 fits into 18 0 times, leaving a remainder of 18.
Use 0 as the next digit of our solution. 
Result so far: 1170.0
Subtracting 0 from 18 leaves us with 18.
Grab the next digit (4) from the dividend, add it to 18, then carry on: 184 / 35

Going ahead to step 6:
If we divide 184 by 35, we get 5 and a remainder of 9.
The number 5 becomes the next digit in our result. 
Result so far: 11705.0
The remainder is 9 after subtracting 175 from 184.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 7:
If we divide 90 by 35, we get 2 and a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 11705.2
Subtract 70 from 90 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.

Going ahead to step 8:
35 goes into 200 5 times with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 11705.25
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.

Advancing to step 9:
When dividing 250 by 35, we get 7 with a remainder of 5.
Use 7 as the next digit of our solution. 
Result so far: 11705.257
If we take 245 away from 250, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 10:
50 divided by 35 is 1 with a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 11705.2571
Subtracting 35 from 50 leaves us with 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 11:
150 divided by 35 is 4 with a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 11705.25714
Subtracting 140 from 150 leaves us 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.

Going ahead to step 12:
35 goes into 100 2 times with a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 11705.257142
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.

Going ahead to step 13:
If we divide 300 by 35, we get 8 and a remainder of 20.
Put 8 as the next digit of the answer. 
Result so far: 11705.2571428
The remainder is 20 after subtracting 280 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 14:
35 goes into 200 5 times with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 11705.25714285
Subtracting 175 from 200 leaves us 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.

The final result is 11705.25714285 with a remainder of 2.5e-08.