35361 ÷ 4 
We're looking to find how many times 4 goes into 35361.

Step 1:
The number 4 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 4

Step 2:
35 divided by 4 is 8 with a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Deduct 32 from 35 and we're left with 3.
Take the next digit (3) from the dividend and append it to 3, then repeat: 33 / 4

Moving on to step 3:
33 divided by 4 is 8 with a remainder of 1.
Write down 8 as next digit of the result. 
Result so far: 88.0
Deduct 32 from 33 and we're left with 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Advancing to step 4:
If we divide 16 by 4, we get 4 and a remainder of 0.
Write down 4 as next digit of the result. 
Result so far: 884.0
The remainder is 0 after subtracting 16 from 16.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 4

Advancing to step 5:
1 divided by 4 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 8840.0
Deduct 0 from 1 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 6:
The number 4 fits into 10 2 times, leaving a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 8840.2
If we subtract 8 from 10, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
When dividing 20 by 4, we get 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 8840.25
The remainder is 0 after subtracting 20 from 20.
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 8:
0 divided by 4 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 8840.25
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:
The number 4 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 8840.25
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 8840.25 and a remainder of 0.0.