583668 ÷ 35 
Our goal is to divide 583668 by 35.

Going ahead to step 1:
35 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 35

Advancing to step 2:
58 divided by 35 is 1 with a remainder of 23.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 35 from 58 and we're left with 23.
Include the next digit (3) from the dividend after 23, then repeat: 233 / 35

Advancing to step 3:
When dividing 233 by 35, we get 6 with a remainder of 23.
The next digit of our result is 6. 
Result so far: 16.0
The remainder is 23 after subtracting 210 from 233.
Take the next digit (6) from the dividend and append it to 23, then repeat: 236 / 35

On to step 4:
236 divided by 35 is 6 with a remainder of 26.
The number 6 becomes the next digit in our result. 
Result so far: 166.0
If we subtract 210 from 236, we get 26.
Grab the next digit (6) from the dividend, add it to 26, then carry on: 266 / 35

Let's proceed to step 5:
When dividing 266 by 35, we get 7 with a remainder of 21.
Write down 7 as next digit of the result. 
Result so far: 1667.0
If we subtract 245 from 266, we get 21.
Grab the next digit (8) from the dividend, add it to 21, then carry on: 218 / 35

Let's proceed to step 6:
When dividing 218 by 35, we get 6 with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 16676.0
If we take 210 away from 218, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 7:
The number 35 fits into 80 2 times, leaving a remainder of 10.
The next digit of our result is 2. 
Result so far: 16676.2
If we take 70 away from 80, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 8:
35 goes into 100 2 times with a remainder of 30.
The number 2 becomes the next digit in our result. 
Result so far: 16676.22
Subtracting 70 from 100 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.

After the division, we end up with 16676.22 and a remainder of 0.03.