We look at the division of 508417 by 35 
We're looking to find how many times 35 goes into 508417.

Moving on to step 1:
When dividing 5 by 35, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 35

On to step 2:
If we divide 50 by 35, we get 1 and a remainder of 15.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 15 after subtracting 35 from 50.
Include the next digit (8) from the dividend after 15, then repeat: 158 / 35

Step 3:
If we divide 158 by 35, we get 4 and a remainder of 18.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
If we take 140 away from 158, we end up with 18.
Bring next digit (4) of the dividend behind the 18 and repeat the process: 184 / 35

Going ahead to step 4:
35 can be fit into 184 5 times, resulting in a remainder of 9.
Use 5 as the next digit of our solution. 
Result so far: 145.0
If we take 175 away from 184, we end up with 9.
Include the next digit (1) from the dividend after 9, then repeat: 91 / 35

Step 5:
If we divide 91 by 35, we get 2 and a remainder of 21.
The next digit of our result is 2. 
Result so far: 1452.0
If we subtract 70 from 91, we get 21.
Take the next digit (7) from the dividend and append it to 21, then repeat: 217 / 35

Advancing to step 6:
35 goes into 217 6 times with a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 14526.0
The remainder is 7 after subtracting 210 from 217.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 7:
35 goes into 70 2 times with a remainder of 0.
Write down 2 as next digit of the result. 
Result so far: 14526.2
The remainder is 0 after subtracting 70 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 8:
When dividing 0 by 35, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 14526.2
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 9:
When dividing 0 by 35, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 14526.2
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 14526.2, with a leftover of 0.0.