101934 ÷ 65 
Our goal is to divide 101934 by 65.

Advancing to step 1:
If we divide 1 by 65, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 65

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
If we take 0 away from 10, we end up with 10.
Grab the next digit (1) from the dividend, add it to 10, then carry on: 101 / 65

Step 3:
If we divide 101 by 65, we get 1 and a remainder of 36.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 65 away from 101, we end up with 36.
Include the next digit (9) from the dividend after 36, then repeat: 369 / 65

Moving on to step 4:
369 divided by 65 is 5 with a remainder of 44.
Write down 5 as next digit of the result. 
Result so far: 15.0
If we subtract 325 from 369, we get 44.
Include the next digit (3) from the dividend after 44, then repeat: 443 / 65

Let's proceed to step 5:
If we divide 443 by 65, we get 6 and a remainder of 53.
The number 6 becomes the next digit in our result. 
Result so far: 156.0
Deduct 390 from 443 and we're left with 53.
Grab the next digit (4) from the dividend, add it to 53, then carry on: 534 / 65

Let's proceed to step 6:
If we divide 534 by 65, we get 8 and a remainder of 14.
Record the quotient 8 as the next digit in the result. 
Result so far: 1568.0
Subtract 520 from 534 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 7:
65 goes into 140 2 times with a remainder of 10.
The number 2 becomes the next digit in our result. 
Result so far: 1568.2
If we subtract 130 from 140, we 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 8:
When dividing 100 by 65, we get 1 with a remainder of 35.
Write down 1 as next digit of the result. 
Result so far: 1568.21
If we take 65 away from 100, 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.

On to step 9:
65 goes into 350 5 times with a remainder of 25.
The next digit of our result is 5. 
Result so far: 1568.215
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.

Advancing to step 10:
65 can be fit into 250 3 times, resulting in a remainder of 55.
Use 3 as the next digit of our solution. 
Result so far: 1568.2153
Subtract 195 from 250 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

On to step 11:
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: 1568.21538
Subtract 520 from 550 to get 30.
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 12:
300 divided by 65 is 4 with a remainder of 40.
Record the quotient 4 as the next digit in the result. 
Result so far: 1568.215384
If we subtract 260 from 300, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 13:
65 can be fit into 400 6 times, resulting in a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 1568.2153846
If we subtract 390 from 400, we 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.

Moving on to step 14:
65 goes into 100 1 times with a remainder of 35.
The number 1 becomes the next digit in our result. 
Result so far: 1568.21538461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

After the division, we end up with 1568.21538461 and a remainder of 3.5e-08.