172314 ÷ 41 
Let's see how many times 41 fits into 172314.

Step 1:
1 divided by 41 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 41

Step 2:
17 divided by 41 is 0 with a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Fetch the next digit (2) from the dividend, attach it to 17 and continue: 172 / 41

Step 3:
41 goes into 172 4 times with a remainder of 8.
The next digit of our result is 4. 
Result so far: 4.0
If we take 164 away from 172, we end up with 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 41

Going ahead to step 4:
If we divide 83 by 41, we get 2 and a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 42.0
Subtracting 82 from 83 leaves us with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 41

On to step 5:
41 can be fit into 11 0 times, resulting in a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 420.0
If we take 0 away from 11, we end up with 11.
Append the next digit (4) from the dividend to 11 and continue with: 114 / 41

Advancing to step 6:
The number 41 fits into 114 2 times, leaving a remainder of 32.
The next digit of our result is 2. 
Result so far: 4202.0
The remainder is 32 after subtracting 82 from 114.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 7:
The number 41 fits into 320 7 times, leaving a remainder of 33.
Put 7 as the next digit of the answer. 
Result so far: 4202.7
Deduct 287 from 320 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Let's proceed to step 8:
If we divide 330 by 41, we get 8 and a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 4202.78
The remainder is 2 after subtracting 328 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 9:
41 goes into 20 0 times with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 4202.78
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 10:
If we divide 200 by 41, we get 4 and a remainder of 36.
Use 4 as the next digit of our solution. 
Result so far: 4202.7804
Subtracting 164 from 200 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 11:
When dividing 360 by 41, we get 8 with a remainder of 32.
Record the quotient 8 as the next digit in the result. 
Result so far: 4202.78048
The remainder is 32 after subtracting 328 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 12:
When dividing 320 by 41, we get 7 with a remainder of 33.
The number 7 becomes the next digit in our result. 
Result so far: 4202.780487
If we take 287 away from 320, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 13:
41 goes into 330 8 times with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 4202.7804878
Deduct 328 from 330 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 14:
When dividing 20 by 41, we get 0 with a remainder of 20.
The next digit of our result is 0. 
Result so far: 4202.7804878
Subtracting 0 from 20 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 4202.7804878 and a remainder of 2e-08.