We're dividing 171001 by 35 
We're looking to find how many times 35 goes into 171001.

Going ahead to step 1:
If we divide 1 by 35, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 35

On to step 2:
When dividing 17 by 35, we get 0 with a remainder of 17.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Bring next digit (1) of the dividend behind the 17 and repeat the process: 171 / 35

Step 3:
The number 35 fits into 171 4 times, leaving a remainder of 31.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
If we take 140 away from 171, we end up with 31.
Grab the next digit (0) from the dividend, add it to 31, then carry on: 310 / 35

Step 4:
310 divided by 35 is 8 with a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 48.0
If we subtract 280 from 310, we get 30.
Include the next digit (0) from the dividend after 30, then repeat: 300 / 35

Let's proceed to step 5:
The number 35 fits into 300 8 times, leaving a remainder of 20.
Use 8 as the next digit of our solution. 
Result so far: 488.0
The remainder is 20 after subtracting 280 from 300.
Include the next digit (1) from the dividend after 20, then repeat: 201 / 35

Advancing to step 6:
35 can be fit into 201 5 times, resulting in a remainder of 26.
The next digit of our result is 5. 
Result so far: 4885.0
Subtracting 175 from 201 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 7:
260 divided by 35 is 7 with a remainder of 15.
Use 7 as the next digit of our solution. 
Result so far: 4885.7
Subtracting 245 from 260 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.

Advancing to step 8:
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: 4885.74
If we subtract 140 from 150, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
35 can be fit into 100 2 times, resulting in a remainder of 30.
Write down 2 as next digit of the result. 
Result so far: 4885.742
Subtract 70 from 100 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 10:
300 divided by 35 is 8 with a remainder of 20.
Write down 8 as next digit of the result. 
Result so far: 4885.7428
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.

Moving on to step 11:
If we divide 200 by 35, we get 5 and a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 4885.74285
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.

On to step 12:
35 goes into 250 7 times with a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 4885.742857
Deduct 245 from 250 and we're left 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.

Advancing to step 13:
50 divided by 35 is 1 with a remainder of 15.
Write down 1 as next digit of the result. 
Result so far: 4885.7428571
If we subtract 35 from 50, we 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.

Moving on to step 14:
When dividing 150 by 35, we get 4 with a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 4885.74285714
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.

The final result is 4885.74285714 with a remainder of 1e-08.