We're dividing 362421 by 35 
We're looking to find how many times 35 goes into 362421.

Step 1:
35 goes into 3 0 times with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 35

Advancing to step 2:
If we divide 36 by 35, we get 1 and a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 35 from 36 and we're left with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 35

On to step 3:
When dividing 12 by 35, we get 0 with a remainder of 12.
Put 0 as the next digit of the answer. 
Result so far: 10.0
If we subtract 0 from 12, we get 12.
Bring next digit (4) of the dividend behind the 12 and repeat the process: 124 / 35

Moving on to step 4:
35 can be fit into 124 3 times, resulting in a remainder of 19.
The number 3 becomes the next digit in our result. 
Result so far: 103.0
If we subtract 105 from 124, we get 19.
Bring next digit (2) of the dividend behind the 19 and repeat the process: 192 / 35

Advancing to step 5:
If we divide 192 by 35, we get 5 and a remainder of 17.
Record the quotient 5 as the next digit in the result. 
Result so far: 1035.0
If we take 175 away from 192, we end up with 17.
Append the next digit (1) from the dividend to 17 and continue with: 171 / 35

Let's proceed to step 6:
171 divided by 35 is 4 with a remainder of 31.
Use 4 as the next digit of our solution. 
Result so far: 10354.0
Subtracting 140 from 171 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.

Step 7:
35 can be fit into 310 8 times, resulting in a remainder of 30.
The number 8 becomes the next digit in our result. 
Result so far: 10354.8
If we subtract 280 from 310, 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 8:
The number 35 fits into 300 8 times, leaving a remainder of 20.
Write down 8 as next digit of the result. 
Result so far: 10354.88
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 10354.88 and a remainder of 0.02.