We're dividing 419187 by 71 
We want to divide 419187 by 71.

Step 1:
When dividing 4 by 71, we get 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 71

Going ahead to step 2:
When dividing 41 by 71, we get 0 with a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 41 leaves us with 41.
Include the next digit (9) from the dividend after 41, then repeat: 419 / 71

Step 3:
When dividing 419 by 71, we get 5 with a remainder of 64.
Put 5 as the next digit of the answer. 
Result so far: 5.0
If we take 355 away from 419, we end up with 64.
Append the next digit (1) from the dividend to 64 and continue with: 641 / 71

Step 4:
641 divided by 71 is 9 with a remainder of 2.
Write down 9 as next digit of the result. 
Result so far: 59.0
If we subtract 639 from 641, we get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 71

Going ahead to step 5:
When dividing 28 by 71, we get 0 with a remainder of 28.
The number 0 becomes the next digit in our result. 
Result so far: 590.0
Subtracting 0 from 28 leaves us with 28.
Bring next digit (7) of the dividend behind the 28 and repeat the process: 287 / 71

Advancing to step 6:
The number 71 fits into 287 4 times, leaving a remainder of 3.
The number 4 becomes the next digit in our result. 
Result so far: 5904.0
Subtracting 284 from 287 leaves us 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.

Going ahead to step 7:
The number 71 fits into 30 0 times, leaving a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 5904.0
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.

Advancing to step 8:
When dividing 300 by 71, we get 4 with a remainder of 16.
Write down 4 as next digit of the result. 
Result so far: 5904.04
Deduct 284 from 300 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 9:
The number 71 fits into 160 2 times, leaving a remainder of 18.
The next digit of our result is 2. 
Result so far: 5904.042
Subtracting 142 from 160 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 10:
71 goes into 180 2 times with a remainder of 38.
The next digit of our result is 2. 
Result so far: 5904.0422
Subtracting 142 from 180 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Our division results in 5904.0422 with a remaining 0.00038.