We look at the division of 419421 by 31 
Our goal is to divide 419421 by 31.

Moving on to step 1:
If we divide 4 by 31, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 31

On to step 2:
The number 31 fits into 41 1 times, leaving a remainder of 10.
The next digit of our result is 1. 
Result so far: 1.0
If we take 31 away from 41, we end up with 10.
Grab the next digit (9) from the dividend, add it to 10, then carry on: 109 / 31

Step 3:
When dividing 109 by 31, we get 3 with a remainder of 16.
Put 3 as the next digit of the answer. 
Result so far: 13.0
Subtract 93 from 109 to get 16.
Bring next digit (4) of the dividend behind the 16 and repeat the process: 164 / 31

Moving on to step 4:
31 goes into 164 5 times with a remainder of 9.
Put 5 as the next digit of the answer. 
Result so far: 135.0
The remainder is 9 after subtracting 155 from 164.
Grab the next digit (2) from the dividend, add it to 9, then carry on: 92 / 31

Step 5:
If we divide 92 by 31, we get 2 and a remainder of 30.
Use 2 as the next digit of our solution. 
Result so far: 1352.0
Subtracting 62 from 92 leaves us with 30.
Include the next digit (1) from the dividend after 30, then repeat: 301 / 31

On to step 6:
If we divide 301 by 31, we get 9 and a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 13529.0
Subtracting 279 from 301 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 7:
The number 31 fits into 220 7 times, leaving a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 13529.7
Deduct 217 from 220 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 8:
31 goes into 30 0 times with a remainder of 30.
The next digit of our result is 0. 
Result so far: 13529.7
Subtracting 0 from 30 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.

Step 9:
31 can be fit into 300 9 times, resulting in a remainder of 21.
Write down 9 as next digit of the result. 
Result so far: 13529.709
The remainder is 21 after subtracting 279 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 10:
If we divide 210 by 31, we get 6 and a remainder of 24.
The next digit of our result is 6. 
Result so far: 13529.7096
If we subtract 186 from 210, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 11:
The number 31 fits into 240 7 times, leaving a remainder of 23.
The number 7 becomes the next digit in our result. 
Result so far: 13529.70967
If we subtract 217 from 240, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 12:
The number 31 fits into 230 7 times, leaving a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 13529.709677
Subtract 217 from 230 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 13529.709677 with a balance of 1.3e-06.