We look at the division of 35872609 by 419 
We want to divide 35872609 by 419.

On to step 1:
The number 419 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 419

On to step 2:
The number 419 fits into 35 0 times, leaving a remainder of 35.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 35, we end up with 35.
Append the next digit (8) from the dividend to 35 and continue with: 358 / 419

Going ahead to step 3:
The number 419 fits into 358 0 times, leaving a remainder of 358.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 358 leaves us with 358.
Grab the next digit (7) from the dividend, add it to 358, then carry on: 3587 / 419

Advancing to step 4:
419 goes into 3587 8 times with a remainder of 235.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we subtract 3352 from 3587, we get 235.
Take the next digit (2) from the dividend and append it to 235, then repeat: 2352 / 419

Moving on to step 5:
2352 divided by 419 is 5 with a remainder of 257.
The next digit of our result is 5. 
Result so far: 85.0
If we take 2095 away from 2352, we end up with 257.
Include the next digit (6) from the dividend after 257, then repeat: 2576 / 419

On to step 6:
419 can be fit into 2576 6 times, resulting in a remainder of 62.
The next digit of our result is 6. 
Result so far: 856.0
Deduct 2514 from 2576 and we're left with 62.
Take the next digit (0) from the dividend and append it to 62, then repeat: 620 / 419

Advancing to step 7:
If we divide 620 by 419, we get 1 and a remainder of 201.
Put 1 as the next digit of the answer. 
Result so far: 8561.0
The remainder is 201 after subtracting 419 from 620.
Take the next digit (9) from the dividend and append it to 201, then repeat: 2019 / 419

Advancing to step 8:
2019 divided by 419 is 4 with a remainder of 343.
Use 4 as the next digit of our solution. 
Result so far: 85614.0
Subtracting 1676 from 2019 leaves us with 343.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3430, and continue the process.

Moving on to step 9:
If we divide 3430 by 419, we get 8 and a remainder of 78.
Write down 8 as next digit of the result. 
Result so far: 85614.8
Deduct 3352 from 3430 and we're left with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 10:
When dividing 780 by 419, we get 1 with a remainder of 361.
Put 1 as the next digit of the answer. 
Result so far: 85614.81
The remainder is 361 after subtracting 419 from 780.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3610, and continue the process.

Moving on to step 11:
419 can be fit into 3610 8 times, resulting in a remainder of 258.
The number 8 becomes the next digit in our result. 
Result so far: 85614.818
Subtract 3352 from 3610 to get 258.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2580, and continue the process.

Going ahead to step 12:
The number 419 fits into 2580 6 times, leaving a remainder of 66.
Write down 6 as next digit of the result. 
Result so far: 85614.8186
If we take 2514 away from 2580, we end up with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Step 13:
The number 419 fits into 660 1 times, leaving a remainder of 241.
The next digit of our result is 1. 
Result so far: 85614.81861
If we take 419 away from 660, we end up with 241.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2410, and continue the process.

On to step 14:
419 goes into 2410 5 times with a remainder of 315.
Write down 5 as next digit of the result. 
Result so far: 85614.818615
Subtracting 2095 from 2410 leaves us with 315.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3150, and continue the process.

Moving on to step 15:
If we divide 3150 by 419, we get 7 and a remainder of 217.
Write down 7 as next digit of the result. 
Result so far: 85614.8186157
Subtracting 2933 from 3150 leaves us with 217.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2170, and continue the process.

Moving on to step 16:
419 goes into 2170 5 times with a remainder of 75.
Record the quotient 5 as the next digit in the result. 
Result so far: 85614.81861575
If we take 2095 away from 2170, we end up with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

The final result is 85614.81861575 with a remainder of 7.5e-08.