Let's divide 103109 by 65
We're looking to find how many times 65 goes into 103109.

Step 1:
65 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
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 65

On to step 2:
The number 65 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Take the next digit (3) from the dividend and append it to 10, then repeat: 103 / 65

Advancing to step 3:
65 goes into 103 1 times with a remainder of 38.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 65 away from 103, we end up with 38.
Take the next digit (1) from the dividend and append it to 38, then repeat: 381 / 65

Moving on to step 4:
When dividing 381 by 65, we get 5 with a remainder of 56.
Write down 5 as next digit of the result. 
Result so far: 15.0
If we subtract 325 from 381, we get 56.
Append the next digit (0) from the dividend to 56 and continue with: 560 / 65

Step 5:
65 goes into 560 8 times with a remainder of 40.
Record the quotient 8 as the next digit in the result. 
Result so far: 158.0
If we take 520 away from 560, we end up with 40.
Grab the next digit (9) from the dividend, add it to 40, then carry on: 409 / 65

Going ahead to step 6:
When dividing 409 by 65, we get 6 with a remainder of 19.
Put 6 as the next digit of the answer. 
Result so far: 1586.0
Deduct 390 from 409 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 7:
65 can be fit into 190 2 times, resulting in a remainder of 60.
The number 2 becomes the next digit in our result. 
Result so far: 1586.2
If we subtract 130 from 190, we 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.

Advancing to step 8:
65 goes into 600 9 times with a remainder of 15.
Write down 9 as next digit of the result. 
Result so far: 1586.29
The remainder is 15 after subtracting 585 from 600.
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 9:
If we divide 150 by 65, we get 2 and a remainder of 20.
The next digit of our result is 2. 
Result so far: 1586.292
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 10:
65 goes into 200 3 times with a remainder of 5.
The next digit of our result is 3. 
Result so far: 1586.2923
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.

Let's proceed to step 11:
65 goes into 50 0 times with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 1586.2923
If we subtract 0 from 50, we 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.

Moving on to step 12:
65 can be fit into 500 7 times, resulting in a remainder of 45.
Write down 7 as next digit of the result. 
Result so far: 1586.292307
If we subtract 455 from 500, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 13:
65 goes into 450 6 times with a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 1586.2923076
If we subtract 390 from 450, we 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.

Moving on to step 14:
65 goes into 600 9 times with a remainder of 15.
The next digit of our result is 9. 
Result so far: 1586.29230769
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.

The final result is 1586.29230769 with a remainder of 1.5e-08.