We're dividing 35584145 by 353 
We want to divide 35584145 by 353.

Step 1:
The number 353 fits into 3 0 times, leaving a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 353

On to step 2:
35 divided by 353 is 0 with a remainder of 35.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 35 and we're left with 35.
Bring next digit (5) of the dividend behind the 35 and repeat the process: 355 / 353

Going ahead to step 3:
When dividing 355 by 353, we get 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 353 from 355 to get 2.
Take the next digit (8) from the dividend and append it to 2, then repeat: 28 / 353

Step 4:
28 divided by 353 is 0 with a remainder of 28.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 28 after subtracting 0 from 28.
Take the next digit (4) from the dividend and append it to 28, then repeat: 284 / 353

Let's proceed to step 5:
353 can be fit into 284 0 times, resulting in a remainder of 284.
Record the quotient 0 as the next digit in the result. 
Result so far: 100.0
If we take 0 away from 284, we end up with 284.
Include the next digit (1) from the dividend after 284, then repeat: 2841 / 353

Advancing to step 6:
353 can be fit into 2841 8 times, resulting in a remainder of 17.
The number 8 becomes the next digit in our result. 
Result so far: 1008.0
Subtracting 2824 from 2841 leaves us with 17.
Include the next digit (4) from the dividend after 17, then repeat: 174 / 353

Step 7:
353 can be fit into 174 0 times, resulting in a remainder of 174.
Use 0 as the next digit of our solution. 
Result so far: 10080.0
The remainder is 174 after subtracting 0 from 174.
Grab the next digit (5) from the dividend, add it to 174, then carry on: 1745 / 353

Moving on to step 8:
353 can be fit into 1745 4 times, resulting in a remainder of 333.
Write down 4 as next digit of the result. 
Result so far: 100804.0
If we take 1412 away from 1745, we end up with 333.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3330, and continue the process.

Going ahead to step 9:
3330 divided by 353 is 9 with a remainder of 153.
Write down 9 as next digit of the result. 
Result so far: 100804.9
If we subtract 3177 from 3330, we get 153.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1530, and continue the process.

Advancing to step 10:
If we divide 1530 by 353, we get 4 and a remainder of 118.
The number 4 becomes the next digit in our result. 
Result so far: 100804.94
The remainder is 118 after subtracting 1412 from 1530.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1180, and continue the process.

Let's proceed to step 11:
353 goes into 1180 3 times with a remainder of 121.
The next digit of our result is 3. 
Result so far: 100804.943
Subtracting 1059 from 1180 leaves us with 121.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1210, and continue the process.

Step 12:
353 can be fit into 1210 3 times, resulting in a remainder of 151.
Record the quotient 3 as the next digit in the result. 
Result so far: 100804.9433
Deduct 1059 from 1210 and we're left with 151.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1510, and continue the process.

The quotient of the division is 100804.9433, and the remainder is 0.00151.