We look at the division of 413431 by 88 
We're looking to find how many times 88 goes into 413431.

Going ahead to step 1:
4 divided by 88 is 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 88

Going ahead to step 2:
If we divide 41 by 88, we get 0 and a remainder of 41.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 41, we get 41.
Take the next digit (3) from the dividend and append it to 41, then repeat: 413 / 88

Going ahead to step 3:
When dividing 413 by 88, we get 4 with a remainder of 61.
The next digit of our result is 4. 
Result so far: 4.0
Deduct 352 from 413 and we're left with 61.
Append the next digit (4) from the dividend to 61 and continue with: 614 / 88

On to step 4:
88 can be fit into 614 6 times, resulting in a remainder of 86.
Use 6 as the next digit of our solution. 
Result so far: 46.0
The remainder is 86 after subtracting 528 from 614.
Grab the next digit (3) from the dividend, add it to 86, then carry on: 863 / 88

Step 5:
When dividing 863 by 88, we get 9 with a remainder of 71.
Use 9 as the next digit of our solution. 
Result so far: 469.0
Deduct 792 from 863 and we're left with 71.
Include the next digit (1) from the dividend after 71, then repeat: 711 / 88

Step 6:
If we divide 711 by 88, we get 8 and a remainder of 7.
The number 8 becomes the next digit in our result. 
Result so far: 4698.0
The remainder is 7 after subtracting 704 from 711.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
If we divide 70 by 88, we get 0 and a remainder of 70.
Put 0 as the next digit of the answer. 
Result so far: 4698.0
Subtract 0 from 70 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Advancing to step 8:
If we divide 700 by 88, we get 7 and a remainder of 84.
Write down 7 as next digit of the result. 
Result so far: 4698.07
Subtracting 616 from 700 leaves us with 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

Step 9:
840 divided by 88 is 9 with a remainder of 48.
Put 9 as the next digit of the answer. 
Result so far: 4698.079
Subtracting 792 from 840 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Going ahead to step 10:
The number 88 fits into 480 5 times, leaving a remainder of 40.
The next digit of our result is 5. 
Result so far: 4698.0795
Subtract 440 from 480 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 11:
The number 88 fits into 400 4 times, leaving a remainder of 48.
Use 4 as the next digit of our solution. 
Result so far: 4698.07954
If we take 352 away from 400, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Advancing to step 12:
When dividing 480 by 88, we get 5 with a remainder of 40.
The number 5 becomes the next digit in our result. 
Result so far: 4698.079545
Subtract 440 from 480 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 13:
88 goes into 400 4 times with a remainder of 48.
Write down 4 as next digit of the result. 
Result so far: 4698.0795454
If we take 352 away from 400, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 14:
88 goes into 480 5 times with a remainder of 40.
Record the quotient 5 as the next digit in the result. 
Result so far: 4698.07954545
If we subtract 440 from 480, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The final result is 4698.07954545 with a remainder of 4e-08.