We're dividing 109172 by 65 
Our goal is to divide 109172 by 65.

Advancing to step 1:
If we divide 1 by 65, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 65

Going ahead to step 2:
65 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 65

On to step 3:
If we divide 109 by 65, we get 1 and a remainder of 44.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 65 from 109 to get 44.
Append the next digit (1) from the dividend to 44 and continue with: 441 / 65

Advancing to step 4:
If we divide 441 by 65, we get 6 and a remainder of 51.
Record the quotient 6 as the next digit in the result. 
Result so far: 16.0
The remainder is 51 after subtracting 390 from 441.
Bring next digit (7) of the dividend behind the 51 and repeat the process: 517 / 65

Step 5:
65 can be fit into 517 7 times, resulting in a remainder of 62.
Record the quotient 7 as the next digit in the result. 
Result so far: 167.0
Deduct 455 from 517 and we're left with 62.
Fetch the next digit (2) from the dividend, attach it to 62 and continue: 622 / 65

Going ahead to step 6:
622 divided by 65 is 9 with a remainder of 37.
Write down 9 as next digit of the result. 
Result so far: 1679.0
Subtracting 585 from 622 leaves us with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Moving on to step 7:
The number 65 fits into 370 5 times, leaving a remainder of 45.
Put 5 as the next digit of the answer. 
Result so far: 1679.5
Deduct 325 from 370 and we're left 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.

Advancing to step 8:
450 divided by 65 is 6 with a remainder of 60.
The number 6 becomes the next digit in our result. 
Result so far: 1679.56
The remainder is 60 after subtracting 390 from 450.
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 goes into 600 9 times with a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 1679.569
If we take 585 away from 600, 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.

Moving on to step 10:
The number 65 fits into 150 2 times, leaving a remainder of 20.
Write down 2 as next digit of the result. 
Result so far: 1679.5692
The remainder is 20 after subtracting 130 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 11:
65 can be fit into 200 3 times, resulting in a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 1679.56923
If we take 195 away from 200, we end up with 5.
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:
The number 65 fits into 50 0 times, leaving a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 1679.56923
Subtracting 0 from 50 leaves us 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.

Step 13:
The number 65 fits into 500 7 times, leaving a remainder of 45.
Record the quotient 7 as the next digit in the result. 
Result so far: 1679.5692307
Deduct 455 from 500 and we're left 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.

Let's proceed to step 14:
When dividing 450 by 65, we get 6 with a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 1679.56923076
If we take 390 away from 450, we end up 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 result is 1679.56923076 with a remainder of 6e-08.