We're dividing 175974 by 35 
We're looking to find how many times 35 goes into 175974.

Let's proceed to step 1:
35 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 35

Going ahead to step 2:
35 can be fit into 17 0 times, resulting in a remainder of 17.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Append the next digit (5) from the dividend to 17 and continue with: 175 / 35

Going ahead to step 3:
When dividing 175 by 35, we get 5 with a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtracting 175 from 175 leaves us with 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 35

Going ahead to step 4:
If we divide 9 by 35, we get 0 and a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 50.0
Deduct 0 from 9 and we're left with 9.
Fetch the next digit (7) from the dividend, attach it to 9 and continue: 97 / 35

On to step 5:
The number 35 fits into 97 2 times, leaving a remainder of 27.
Record the quotient 2 as the next digit in the result. 
Result so far: 502.0
Subtract 70 from 97 to get 27.
Fetch the next digit (4) from the dividend, attach it to 27 and continue: 274 / 35

Advancing to step 6:
When dividing 274 by 35, we get 7 with a remainder of 29.
The next digit of our result is 7. 
Result so far: 5027.0
Subtracting 245 from 274 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 7:
The number 35 fits into 290 8 times, leaving a remainder of 10.
The number 8 becomes the next digit in our result. 
Result so far: 5027.8
If we take 280 away from 290, we end up 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.

Step 8:
35 goes into 100 2 times with a remainder of 30.
Put 2 as the next digit of the answer. 
Result so far: 5027.82
If we subtract 70 from 100, we 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.

Moving on to step 9:
When dividing 300 by 35, we get 8 with a remainder of 20.
Put 8 as the next digit of the answer. 
Result so far: 5027.828
If we subtract 280 from 300, we 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.

Moving on to step 10:
If we divide 200 by 35, we get 5 and a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 5027.8285
Subtract 175 from 200 to get 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 11:
250 divided by 35 is 7 with a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 5027.82857
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.

Going ahead to step 12:
35 can be fit into 50 1 times, resulting in a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 5027.828571
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 13:
The number 35 fits into 150 4 times, leaving a remainder of 10.
Record the quotient 4 as the next digit in the result. 
Result so far: 5027.8285714
The remainder is 10 after subtracting 140 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 14:
35 goes into 100 2 times with a remainder of 30.
The next digit of our result is 2. 
Result so far: 5027.82857142
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.

The final outcome is 5027.82857142, with a leftover of 3e-08.