We're dividing 101825 by 65 
We want to divide 101825 by 65.

Let's proceed to step 1:
If we divide 1 by 65, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 65

On to step 2:
10 divided by 65 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 65

Let's proceed to step 3:
When dividing 101 by 65, we get 1 with a remainder of 36.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 65 from 101, we get 36.
Fetch the next digit (8) from the dividend, attach it to 36 and continue: 368 / 65

Going ahead to step 4:
65 can be fit into 368 5 times, resulting in a remainder of 43.
Write down 5 as next digit of the result. 
Result so far: 15.0
Subtracting 325 from 368 leaves us with 43.
Fetch the next digit (2) from the dividend, attach it to 43 and continue: 432 / 65

On to step 5:
If we divide 432 by 65, we get 6 and a remainder of 42.
Use 6 as the next digit of our solution. 
Result so far: 156.0
If we subtract 390 from 432, we get 42.
Take the next digit (5) from the dividend and append it to 42, then repeat: 425 / 65

Moving on to step 6:
425 divided by 65 is 6 with a remainder of 35.
Use 6 as the next digit of our solution. 
Result so far: 1566.0
If we take 390 away from 425, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 7:
If we divide 350 by 65, we get 5 and a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 1566.5
Subtracting 325 from 350 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 8:
65 goes into 250 3 times with a remainder of 55.
Use 3 as the next digit of our solution. 
Result so far: 1566.53
Subtracting 195 from 250 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 9:
When dividing 550 by 65, we get 8 with a remainder of 30.
Use 8 as the next digit of our solution. 
Result so far: 1566.538
The remainder is 30 after subtracting 520 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 10:
The number 65 fits into 300 4 times, leaving a remainder of 40.
Use 4 as the next digit of our solution. 
Result so far: 1566.5384
Subtracting 260 from 300 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 11:
400 divided by 65 is 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 1566.53846
Subtract 390 from 400 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 12:
The number 65 fits into 100 1 times, leaving a remainder of 35.
Put 1 as the next digit of the answer. 
Result so far: 1566.538461
The remainder is 35 after subtracting 65 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 13:
65 can be fit into 350 5 times, resulting in a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 1566.5384615
Deduct 325 from 350 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 14:
The number 65 fits into 250 3 times, leaving a remainder of 55.
The number 3 becomes the next digit in our result. 
Result so far: 1566.53846153
Deduct 195 from 250 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

The final outcome is 1566.53846153, with a leftover of 5.5e-08.