253361 ÷ 35 
We're looking to find how many times 35 goes into 253361.

Let's proceed to step 1:
If we divide 2 by 35, we get 0 and a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 35

Step 2:
35 goes into 25 0 times with a remainder of 25.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 25, we get 25.
Bring next digit (3) of the dividend behind the 25 and repeat the process: 253 / 35

Moving on to step 3:
If we divide 253 by 35, we get 7 and a remainder of 8.
The next digit of our result is 7. 
Result so far: 7.0
Subtracting 245 from 253 leaves us with 8.
Take the next digit (3) from the dividend and append it to 8, then repeat: 83 / 35

On to step 4:
If we divide 83 by 35, we get 2 and a remainder of 13.
Put 2 as the next digit of the answer. 
Result so far: 72.0
The remainder is 13 after subtracting 70 from 83.
Take the next digit (6) from the dividend and append it to 13, then repeat: 136 / 35

Moving on to step 5:
136 divided by 35 is 3 with a remainder of 31.
The number 3 becomes the next digit in our result. 
Result so far: 723.0
If we subtract 105 from 136, we get 31.
Fetch the next digit (1) from the dividend, attach it to 31 and continue: 311 / 35

Moving on to step 6:
35 can be fit into 311 8 times, resulting in a remainder of 31.
The number 8 becomes the next digit in our result. 
Result so far: 7238.0
Subtracting 280 from 311 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 7:
35 can be fit into 310 8 times, resulting in a remainder of 30.
The next digit of our result is 8. 
Result so far: 7238.8
Subtracting 280 from 310 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.

Advancing to step 8:
When dividing 300 by 35, we get 8 with a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 7238.88
Deduct 280 from 300 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 7238.88 and a remainder of 0.02.