105175 ÷ 65 
Let's see how many times 65 fits into 105175.

Going ahead to step 1:
When dividing 1 by 65, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 65

Going ahead to step 2:
65 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 65

Step 3:
When dividing 105 by 65, we get 1 with a remainder of 40.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 65 away from 105, we end up with 40.
Take the next digit (1) from the dividend and append it to 40, then repeat: 401 / 65

Advancing to step 4:
When dividing 401 by 65, we get 6 with a remainder of 11.
Put 6 as the next digit of the answer. 
Result so far: 16.0
Deduct 390 from 401 and we're left with 11.
Append the next digit (7) from the dividend to 11 and continue with: 117 / 65

Going ahead to step 5:
65 can be fit into 117 1 times, resulting in a remainder of 52.
The number 1 becomes the next digit in our result. 
Result so far: 161.0
Subtract 65 from 117 to get 52.
Take the next digit (5) from the dividend and append it to 52, then repeat: 525 / 65

Going ahead to step 6:
65 can be fit into 525 8 times, resulting in a remainder of 5.
Record the quotient 8 as the next digit in the result. 
Result so far: 1618.0
The remainder is 5 after subtracting 520 from 525.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 7:
When dividing 50 by 65, we get 0 with a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 1618.0
Subtract 0 from 50 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.

Moving on to step 8:
500 divided by 65 is 7 with a remainder of 45.
The number 7 becomes the next digit in our result. 
Result so far: 1618.07
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.

Let's proceed to step 9:
450 divided by 65 is 6 with a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 1618.076
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.

Moving on to step 10:
When dividing 600 by 65, we get 9 with a remainder of 15.
The next digit of our result is 9. 
Result so far: 1618.0769
Subtracting 585 from 600 leaves us 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 11:
150 divided by 65 is 2 with a remainder of 20.
The next digit of our result is 2. 
Result so far: 1618.07692
If we subtract 130 from 150, we 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 12:
65 goes into 200 3 times with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 1618.076923
Deduct 195 from 200 and we're left 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 13:
The number 65 fits into 50 0 times, leaving a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 1618.076923
Deduct 0 from 50 and we're left 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 14:
65 can be fit into 500 7 times, resulting in a remainder of 45.
The next digit of our result is 7. 
Result so far: 1618.07692307
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.

In conclusion, the division gives 1618.07692307 with a balance of 4.5e-08.