We're dividing 17219 by 41 
We're looking to find how many times 41 goes into 17219.

Moving on to step 1:
When dividing 1 by 41, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 41

On to step 2:
41 can be fit into 17 0 times, resulting in a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 17, we get 17.
Grab the next digit (2) from the dividend, add it to 17, then carry on: 172 / 41

On to step 3:
The number 41 fits into 172 4 times, leaving a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
The remainder is 8 after subtracting 164 from 172.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 41

Step 4:
When dividing 81 by 41, we get 1 with a remainder of 40.
Record the quotient 1 as the next digit in the result. 
Result so far: 41.0
If we subtract 41 from 81, we get 40.
Append the next digit (9) from the dividend to 40 and continue with: 409 / 41

Step 5:
41 can be fit into 409 9 times, resulting in a remainder of 40.
Use 9 as the next digit of our solution. 
Result so far: 419.0
Deduct 369 from 409 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 6:
When dividing 400 by 41, we get 9 with a remainder of 31.
Put 9 as the next digit of the answer. 
Result so far: 419.9
Subtracting 369 from 400 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 7:
If we divide 310 by 41, we get 7 and a remainder of 23.
Write down 7 as next digit of the result. 
Result so far: 419.97
Deduct 287 from 310 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 8:
When dividing 230 by 41, we get 5 with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 419.975
Subtract 205 from 230 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 9:
41 goes into 250 6 times with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 419.9756
If we take 246 away from 250, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 10:
If we divide 40 by 41, we get 0 and a remainder of 40.
The next digit of our result is 0. 
Result so far: 419.9756
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 11:
400 divided by 41 is 9 with a remainder of 31.
Write down 9 as next digit of the result. 
Result so far: 419.975609
If we subtract 369 from 400, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Moving on to step 12:
The number 41 fits into 310 7 times, leaving a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 419.9756097
Deduct 287 from 310 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 13:
The number 41 fits into 230 5 times, leaving a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 419.97560975
Subtract 205 from 230 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Our division results in 419.97560975 with a remaining 2.5e-08.