We look at the division of 100601 by 35 
We want to figure out the number of times 100601 can be divided by 35.

On to step 1:
35 goes into 1 0 times with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 35

Step 2:
10 divided by 35 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Bring next digit (0) of the dividend behind the 10 and repeat the process: 100 / 35

Step 3:
The number 35 fits into 100 2 times, leaving a remainder of 30.
The next digit of our result is 2. 
Result so far: 2.0
If we take 70 away from 100, we end up with 30.
Take the next digit (6) from the dividend and append it to 30, then repeat: 306 / 35

Advancing to step 4:
35 goes into 306 8 times with a remainder of 26.
The number 8 becomes the next digit in our result. 
Result so far: 28.0
The remainder is 26 after subtracting 280 from 306.
Grab the next digit (0) from the dividend, add it to 26, then carry on: 260 / 35

Going ahead to step 5:
When dividing 260 by 35, we get 7 with a remainder of 15.
Record the quotient 7 as the next digit in the result. 
Result so far: 287.0
Deduct 245 from 260 and we're left with 15.
Take the next digit (1) from the dividend and append it to 15, then repeat: 151 / 35

Moving on to step 6:
When dividing 151 by 35, we get 4 with a remainder of 11.
The number 4 becomes the next digit in our result. 
Result so far: 2874.0
The remainder is 11 after subtracting 140 from 151.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 7:
When dividing 110 by 35, we get 3 with a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 2874.3
If we subtract 105 from 110, we get 5.
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 8:
If we divide 50 by 35, we get 1 and a remainder of 15.
Put 1 as the next digit of the answer. 
Result so far: 2874.31
Subtract 35 from 50 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.

Moving on to step 9:
The number 35 fits into 150 4 times, leaving a remainder of 10.
Write down 4 as next digit of the result. 
Result so far: 2874.314
Deduct 140 from 150 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 10:
If we divide 100 by 35, we get 2 and a remainder of 30.
The next digit of our result is 2. 
Result so far: 2874.3142
The remainder is 30 after subtracting 70 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 11:
35 can be fit into 300 8 times, resulting in a remainder of 20.
Put 8 as the next digit of the answer. 
Result so far: 2874.31428
Subtracting 280 from 300 leaves us with 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:
35 goes into 200 5 times with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 2874.314285
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.

Step 13:
The number 35 fits into 250 7 times, leaving a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 2874.3142857
Subtract 245 from 250 to get 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 14:
If we divide 50 by 35, we get 1 and a remainder of 15.
Record the quotient 1 as the next digit in the result. 
Result so far: 2874.31428571
Deduct 35 from 50 and we're left 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.

After the division, we end up with 2874.31428571 and a remainder of 1.5e-08.