We divide 126580 by 17
We want to figure out the number of times 126580 can be divided by 17.

Step 1:
17 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 17

Moving on to step 2:
12 divided by 17 is 0 with a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 12 to get 12.
Include the next digit (6) from the dividend after 12, then repeat: 126 / 17

Step 3:
126 divided by 17 is 7 with a remainder of 7.
The next digit of our result is 7. 
Result so far: 7.0
If we subtract 119 from 126, we get 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 17

Moving on to step 4:
75 divided by 17 is 4 with a remainder of 7.
The number 4 becomes the next digit in our result. 
Result so far: 74.0
Subtract 68 from 75 to get 7.
Fetch the next digit (8) from the dividend, attach it to 7 and continue: 78 / 17

Let's proceed to step 5:
If we divide 78 by 17, we get 4 and a remainder of 10.
Put 4 as the next digit of the answer. 
Result so far: 744.0
Subtract 68 from 78 to get 10.
Bring next digit (0) of the dividend behind the 10 and repeat the process: 100 / 17

Step 6:
17 goes into 100 5 times with a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 7445.0
If we take 85 away from 100, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 7:
The number 17 fits into 150 8 times, leaving a remainder of 14.
Put 8 as the next digit of the answer. 
Result so far: 7445.8
Deduct 136 from 150 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 8:
When dividing 140 by 17, we get 8 with a remainder of 4.
The next digit of our result is 8. 
Result so far: 7445.88
If we subtract 136 from 140, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Our division results in 7445.88 with a remaining 0.004.