We look at the division of 101278 by 35 
We're looking to find how many times 35 goes into 101278.

Going ahead to step 1:
The number 35 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 35

Let's proceed to step 2:
When dividing 10 by 35, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Include the next digit (1) from the dividend after 10, then repeat: 101 / 35

Let's proceed to step 3:
101 divided by 35 is 2 with a remainder of 31.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Deduct 70 from 101 and we're left with 31.
Append the next digit (2) from the dividend to 31 and continue with: 312 / 35

On to step 4:
35 goes into 312 8 times with a remainder of 32.
Put 8 as the next digit of the answer. 
Result so far: 28.0
Subtract 280 from 312 to get 32.
Bring next digit (7) of the dividend behind the 32 and repeat the process: 327 / 35

Let's proceed to step 5:
327 divided by 35 is 9 with a remainder of 12.
Put 9 as the next digit of the answer. 
Result so far: 289.0
Deduct 315 from 327 and we're left with 12.
Fetch the next digit (8) from the dividend, attach it to 12 and continue: 128 / 35

Step 6:
35 can be fit into 128 3 times, resulting in a remainder of 23.
Use 3 as the next digit of our solution. 
Result so far: 2893.0
Deduct 105 from 128 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 7:
The number 35 fits into 230 6 times, leaving a remainder of 20.
Put 6 as the next digit of the answer. 
Result so far: 2893.6
The remainder is 20 after subtracting 210 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 8:
If we divide 200 by 35, we get 5 and a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 2893.65
Deduct 175 from 200 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.

Going ahead to step 9:
250 divided by 35 is 7 with a remainder of 5.
Use 7 as the next digit of our solution. 
Result so far: 2893.657
The remainder is 5 after subtracting 245 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 10:
When dividing 50 by 35, we get 1 with a remainder of 15.
The number 1 becomes the next digit in our result. 
Result so far: 2893.6571
If we take 35 away from 50, 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.

Step 11:
35 goes into 150 4 times with a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 2893.65714
Subtract 140 from 150 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.

On to step 12:
35 can be fit into 100 2 times, resulting in a remainder of 30.
Write down 2 as next digit of the result. 
Result so far: 2893.657142
If we subtract 70 from 100, we 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.

Going ahead to step 13:
35 can be fit into 300 8 times, resulting in a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 2893.6571428
The remainder is 20 after subtracting 280 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 14:
200 divided by 35 is 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 2893.65714285
Subtract 175 from 200 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Our division results in 2893.65714285 with a remaining 2.5e-08.