We look at the division of 10880171 by 419 
Our goal is to divide 10880171 by 419.

Moving on to step 1:
419 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 419

Advancing to step 2:
The number 419 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Grab the next digit (8) from the dividend, add it to 10, then carry on: 108 / 419

Going ahead to step 3:
If we divide 108 by 419, we get 0 and a remainder of 108.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 108 and we're left with 108.
Grab the next digit (8) from the dividend, add it to 108, then carry on: 1088 / 419

Going ahead to step 4:
419 goes into 1088 2 times with a remainder of 250.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 838 from 1088 leaves us with 250.
Grab the next digit (0) from the dividend, add it to 250, then carry on: 2500 / 419

Moving on to step 5:
When dividing 2500 by 419, we get 5 with a remainder of 405.
Use 5 as the next digit of our solution. 
Result so far: 25.0
Subtract 2095 from 2500 to get 405.
Take the next digit (1) from the dividend and append it to 405, then repeat: 4051 / 419

Going ahead to step 6:
If we divide 4051 by 419, we get 9 and a remainder of 280.
The next digit of our result is 9. 
Result so far: 259.0
Subtract 3771 from 4051 to get 280.
Take the next digit (7) from the dividend and append it to 280, then repeat: 2807 / 419

Step 7:
The number 419 fits into 2807 6 times, leaving a remainder of 293.
The number 6 becomes the next digit in our result. 
Result so far: 2596.0
If we take 2514 away from 2807, we end up with 293.
Fetch the next digit (1) from the dividend, attach it to 293 and continue: 2931 / 419

Advancing to step 8:
419 can be fit into 2931 6 times, resulting in a remainder of 417.
Put 6 as the next digit of the answer. 
Result so far: 25966.0
Deduct 2514 from 2931 and we're left with 417.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4170, and continue the process.

Moving on to step 9:
4170 divided by 419 is 9 with a remainder of 399.
Record the quotient 9 as the next digit in the result. 
Result so far: 25966.9
The remainder is 399 after subtracting 3771 from 4170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3990, and continue the process.

Step 10:
3990 divided by 419 is 9 with a remainder of 219.
Put 9 as the next digit of the answer. 
Result so far: 25966.99
Subtract 3771 from 3990 to get 219.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2190, and continue the process.

The final result is 25966.99 with a remainder of 0.219.