We divide 172105 by 65
We're looking to find how many times 65 goes into 172105.

Step 1:
The number 65 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 65

Moving on to step 2:
If we divide 17 by 65, we get 0 and a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Fetch the next digit (2) from the dividend, attach it to 17 and continue: 172 / 65

Advancing to step 3:
If we divide 172 by 65, we get 2 and a remainder of 42.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 130 away from 172, we end up with 42.
Bring next digit (1) of the dividend behind the 42 and repeat the process: 421 / 65

Step 4:
When dividing 421 by 65, we get 6 with a remainder of 31.
The number 6 becomes the next digit in our result. 
Result so far: 26.0
Subtract 390 from 421 to get 31.
Take the next digit (0) from the dividend and append it to 31, then repeat: 310 / 65

Advancing to step 5:
If we divide 310 by 65, we get 4 and a remainder of 50.
Put 4 as the next digit of the answer. 
Result so far: 264.0
The remainder is 50 after subtracting 260 from 310.
Append the next digit (5) from the dividend to 50 and continue with: 505 / 65

Step 6:
The number 65 fits into 505 7 times, leaving a remainder of 50.
Put 7 as the next digit of the answer. 
Result so far: 2647.0
Subtract 455 from 505 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 7:
If we divide 500 by 65, we get 7 and a remainder of 45.
The next digit of our result is 7. 
Result so far: 2647.7
If we take 455 away from 500, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

On to step 8:
When dividing 450 by 65, we get 6 with a remainder of 60.
Write down 6 as next digit of the result. 
Result so far: 2647.76
Subtract 390 from 450 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 9:
65 can be fit into 600 9 times, resulting in a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 2647.769
Subtract 585 from 600 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 10:
If we divide 150 by 65, we get 2 and a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 2647.7692
Subtracting 130 from 150 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.

Let's proceed to step 11:
If we divide 200 by 65, we get 3 and a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 2647.76923
The remainder is 5 after subtracting 195 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 12:
65 goes into 50 0 times with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 2647.76923
If we take 0 away from 50, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 13:
65 can be fit into 500 7 times, resulting in a remainder of 45.
Put 7 as the next digit of the answer. 
Result so far: 2647.7692307
The remainder is 45 after subtracting 455 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 14:
The number 65 fits into 450 6 times, leaving a remainder of 60.
Record the quotient 6 as the next digit in the result. 
Result so far: 2647.76923076
Subtracting 390 from 450 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

The final outcome is 2647.76923076, with a leftover of 6e-08.