456561 ÷ 35 
Our goal is to divide 456561 by 35.

Advancing to step 1:
When dividing 4 by 35, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 35

Going ahead to step 2:
35 goes into 45 1 times with a remainder of 10.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 35 from 45 to get 10.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 35

Step 3:
35 can be fit into 106 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 13.0
The remainder is 1 after subtracting 105 from 106.
Append the next digit (5) from the dividend to 1 and continue with: 15 / 35

Going ahead to step 4:
35 goes into 15 0 times with a remainder of 15.
The next digit of our result is 0. 
Result so far: 130.0
Subtract 0 from 15 to get 15.
Take the next digit (6) from the dividend and append it to 15, then repeat: 156 / 35

Moving on to step 5:
The number 35 fits into 156 4 times, leaving a remainder of 16.
The number 4 becomes the next digit in our result. 
Result so far: 1304.0
If we subtract 140 from 156, we get 16.
Bring next digit (1) of the dividend behind the 16 and repeat the process: 161 / 35

Let's proceed to step 6:
When dividing 161 by 35, we get 4 with a remainder of 21.
Write down 4 as next digit of the result. 
Result so far: 13044.0
If we subtract 140 from 161, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Let's proceed to step 7:
210 divided by 35 is 6 with a remainder of 0.
The number 6 becomes the next digit in our result. 
Result so far: 13044.6
Subtracting 210 from 210 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.

On to step 8:
35 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 13044.6
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.

Moving on to step 9:
The number 35 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 13044.6
Deduct 0 from 0 and we're left 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.

Our division results in 13044.6 with a remaining 0.0.