We're dividing 8589419 by 127 
We're looking to find how many times 127 goes into 8589419.

Moving on to step 1:
127 can be fit into 8 0 times, resulting in a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Grab the next digit (5) from the dividend, add it to 8, then carry on: 85 / 127

Going ahead to step 2:
127 can be fit into 85 0 times, resulting in a remainder of 85.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 85, we get 85.
Bring next digit (8) of the dividend behind the 85 and repeat the process: 858 / 127

On to step 3:
127 can be fit into 858 6 times, resulting in a remainder of 96.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we subtract 762 from 858, we get 96.
Include the next digit (9) from the dividend after 96, then repeat: 969 / 127

Let's proceed to step 4:
127 can be fit into 969 7 times, resulting in a remainder of 80.
The next digit of our result is 7. 
Result so far: 67.0
Subtracting 889 from 969 leaves us with 80.
Grab the next digit (4) from the dividend, add it to 80, then carry on: 804 / 127

Moving on to step 5:
When dividing 804 by 127, we get 6 with a remainder of 42.
Use 6 as the next digit of our solution. 
Result so far: 676.0
Deduct 762 from 804 and we're left with 42.
Take the next digit (1) from the dividend and append it to 42, then repeat: 421 / 127

On to step 6:
127 goes into 421 3 times with a remainder of 40.
The next digit of our result is 3. 
Result so far: 6763.0
Subtracting 381 from 421 leaves us with 40.
Bring next digit (9) of the dividend behind the 40 and repeat the process: 409 / 127

Let's proceed to step 7:
127 can be fit into 409 3 times, resulting in a remainder of 28.
Put 3 as the next digit of the answer. 
Result so far: 67633.0
If we take 381 away from 409, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 8:
280 divided by 127 is 2 with a remainder of 26.
Record the quotient 2 as the next digit in the result. 
Result so far: 67633.2
Deduct 254 from 280 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 9:
If we divide 260 by 127, we get 2 and a remainder of 6.
Put 2 as the next digit of the answer. 
Result so far: 67633.22
If we subtract 254 from 260, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 67633.22 and a remainder of 0.006.