435961 ÷ 31 
Our goal is to divide 435961 by 31.

Step 1:
If we divide 4 by 31, we get 0 and a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 31

Advancing to step 2:
31 goes into 43 1 times with a remainder of 12.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 31 from 43, we get 12.
Grab the next digit (5) from the dividend, add it to 12, then carry on: 125 / 31

Let's proceed to step 3:
31 can be fit into 125 4 times, resulting in a remainder of 1.
The next digit of our result is 4. 
Result so far: 14.0
Subtract 124 from 125 to get 1.
Grab the next digit (9) from the dividend, add it to 1, then carry on: 19 / 31

On to step 4:
If we divide 19 by 31, we get 0 and a remainder of 19.
Record the quotient 0 as the next digit in the result. 
Result so far: 140.0
Subtract 0 from 19 to get 19.
Grab the next digit (6) from the dividend, add it to 19, then carry on: 196 / 31

Let's proceed to step 5:
31 can be fit into 196 6 times, resulting in a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 1406.0
Subtract 186 from 196 to get 10.
Append the next digit (1) from the dividend to 10 and continue with: 101 / 31

On to step 6:
The number 31 fits into 101 3 times, leaving a remainder of 8.
The next digit of our result is 3. 
Result so far: 14063.0
Subtracting 93 from 101 leaves us 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.

Moving on to step 7:
80 divided by 31 is 2 with a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 14063.2
If we subtract 62 from 80, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 8:
31 goes into 180 5 times with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 14063.25
Subtracting 155 from 180 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 9:
The number 31 fits into 250 8 times, leaving a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 14063.258
Subtracting 248 from 250 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 10:
When dividing 20 by 31, we get 0 with a remainder of 20.
The next digit of our result is 0. 
Result so far: 14063.258
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 11:
When dividing 200 by 31, we get 6 with a remainder of 14.
Write down 6 as next digit of the result. 
Result so far: 14063.25806
The remainder is 14 after subtracting 186 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 12:
The number 31 fits into 140 4 times, leaving a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 14063.258064
If we subtract 124 from 140, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 13:
160 divided by 31 is 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 14063.2580645
Subtract 155 from 160 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 14:
If we divide 50 by 31, we get 1 and a remainder of 19.
Use 1 as the next digit of our solution. 
Result so far: 14063.25806451
If we take 31 away from 50, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

After the division, we end up with 14063.25806451 and a remainder of 1.9e-08.