419419 ÷ 88 
Our goal is to divide 419419 by 88.

Step 1:
The number 88 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 88

Step 2:
If we divide 41 by 88, we get 0 and a remainder of 41.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 41 and we're left with 41.
Fetch the next digit (9) from the dividend, attach it to 41 and continue: 419 / 88

Let's proceed to step 3:
88 goes into 419 4 times with a remainder of 67.
The next digit of our result is 4. 
Result so far: 4.0
Subtracting 352 from 419 leaves us with 67.
Take the next digit (4) from the dividend and append it to 67, then repeat: 674 / 88

Moving on to step 4:
When dividing 674 by 88, we get 7 with a remainder of 58.
Put 7 as the next digit of the answer. 
Result so far: 47.0
Subtracting 616 from 674 leaves us with 58.
Grab the next digit (1) from the dividend, add it to 58, then carry on: 581 / 88

Going ahead to step 5:
88 can be fit into 581 6 times, resulting in a remainder of 53.
The next digit of our result is 6. 
Result so far: 476.0
Subtracting 528 from 581 leaves us with 53.
Take the next digit (9) from the dividend and append it to 53, then repeat: 539 / 88

Moving on to step 6:
88 can be fit into 539 6 times, resulting in a remainder of 11.
Use 6 as the next digit of our solution. 
Result so far: 4766.0
If we take 528 away from 539, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 7:
110 divided by 88 is 1 with a remainder of 22.
The number 1 becomes the next digit in our result. 
Result so far: 4766.1
The remainder is 22 after subtracting 88 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 8:
The number 88 fits into 220 2 times, leaving a remainder of 44.
The next digit of our result is 2. 
Result so far: 4766.12
If we subtract 176 from 220, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 9:
88 can be fit into 440 5 times, resulting in a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 4766.125
If we subtract 440 from 440, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
0 divided by 88 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 4766.125
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 11:
If we divide 0 by 88, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 4766.125
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 4766.125, and the remainder is 0.0.