Let's divide 17974 by 35
We want to figure out the number of times 17974 can be divided by 35.

Advancing to step 1:
35 can be fit into 1 0 times, resulting in a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 35

Advancing to step 2:
17 divided by 35 is 0 with a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Fetch the next digit (9) from the dividend, attach it to 17 and continue: 179 / 35

Moving on to step 3:
When dividing 179 by 35, we get 5 with a remainder of 4.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we take 175 away from 179, we end up with 4.
Fetch the next digit (7) from the dividend, attach it to 4 and continue: 47 / 35

Moving on to step 4:
When dividing 47 by 35, we get 1 with a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 51.0
The remainder is 12 after subtracting 35 from 47.
Include the next digit (4) from the dividend after 12, then repeat: 124 / 35

Step 5:
If we divide 124 by 35, we get 3 and a remainder of 19.
Write down 3 as next digit of the result. 
Result so far: 513.0
If we subtract 105 from 124, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 6:
190 divided by 35 is 5 with a remainder of 15.
The next digit of our result is 5. 
Result so far: 513.5
If we subtract 175 from 190, 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.

Step 7:
35 goes into 150 4 times with a remainder of 10.
Write down 4 as next digit of the result. 
Result so far: 513.54
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.

Step 8:
If we divide 100 by 35, we get 2 and a remainder of 30.
Use 2 as the next digit of our solution. 
Result so far: 513.542
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.

Step 9:
If we divide 300 by 35, we get 8 and a remainder of 20.
Write down 8 as next digit of the result. 
Result so far: 513.5428
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.

Moving on to step 10:
If we divide 200 by 35, we get 5 and a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 513.54285
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 11:
The number 35 fits into 250 7 times, leaving a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 513.542857
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.

On to step 12:
If we divide 50 by 35, we get 1 and a remainder of 15.
The next digit of our result is 1. 
Result so far: 513.5428571
If we take 35 away from 50, we end up 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 13:
35 can be fit into 150 4 times, resulting in a remainder of 10.
Record the quotient 4 as the next digit in the result. 
Result so far: 513.54285714
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.

After the division, we end up with 513.54285714 and a remainder of 1e-08.