We look at the division of 370419 by 71 
We want to divide 370419 by 71.

Advancing to step 1:
3 divided by 71 is 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 71

Let's proceed to step 2:
37 divided by 71 is 0 with a remainder of 37.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Take the next digit (0) from the dividend and append it to 37, then repeat: 370 / 71

On to step 3:
If we divide 370 by 71, we get 5 and a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 355 away from 370, we end up with 15.
Append the next digit (4) from the dividend to 15 and continue with: 154 / 71

Moving on to step 4:
154 divided by 71 is 2 with a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 52.0
If we take 142 away from 154, we end up with 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 71

On to step 5:
If we divide 121 by 71, we get 1 and a remainder of 50.
Put 1 as the next digit of the answer. 
Result so far: 521.0
Subtracting 71 from 121 leaves us with 50.
Fetch the next digit (9) from the dividend, attach it to 50 and continue: 509 / 71

Step 6:
509 divided by 71 is 7 with a remainder of 12.
Write down 7 as next digit of the result. 
Result so far: 5217.0
If we take 497 away from 509, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 7:
The number 71 fits into 120 1 times, leaving a remainder of 49.
The next digit of our result is 1. 
Result so far: 5217.1
If we take 71 away from 120, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Step 8:
When dividing 490 by 71, we get 6 with a remainder of 64.
Put 6 as the next digit of the answer. 
Result so far: 5217.16
If we subtract 426 from 490, we get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 9:
When dividing 640 by 71, we get 9 with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 5217.169
Subtracting 639 from 640 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 10:
When dividing 10 by 71, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 5217.169
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 11:
100 divided by 71 is 1 with a remainder of 29.
Write down 1 as next digit of the result. 
Result so far: 5217.16901
Deduct 71 from 100 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 12:
The number 71 fits into 290 4 times, leaving a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 5217.169014
If we take 284 away from 290, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 13:
If we divide 60 by 71, we get 0 and a remainder of 60.
Put 0 as the next digit of the answer. 
Result so far: 5217.169014
Subtracting 0 from 60 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Moving on to step 14:
600 divided by 71 is 8 with a remainder of 32.
Write down 8 as next digit of the result. 
Result so far: 5217.16901408
If we take 568 away from 600, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Our division results in 5217.16901408 with a remaining 3.2e-08.