We look at the division of 35307038 by 681 
We want to divide 35307038 by 681.

On to step 1:
The number 681 fits into 3 0 times, leaving a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 681

Moving on to step 2:
If we divide 35 by 681, we get 0 and a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 35, we get 35.
Bring next digit (3) of the dividend behind the 35 and repeat the process: 353 / 681

Step 3:
When dividing 353 by 681, we get 0 with a remainder of 353.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 353, we end up with 353.
Take the next digit (0) from the dividend and append it to 353, then repeat: 3530 / 681

Going ahead to step 4:
If we divide 3530 by 681, we get 5 and a remainder of 125.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Deduct 3405 from 3530 and we're left with 125.
Take the next digit (7) from the dividend and append it to 125, then repeat: 1257 / 681

Moving on to step 5:
If we divide 1257 by 681, we get 1 and a remainder of 576.
Record the quotient 1 as the next digit in the result. 
Result so far: 51.0
Deduct 681 from 1257 and we're left with 576.
Fetch the next digit (0) from the dividend, attach it to 576 and continue: 5760 / 681

Let's proceed to step 6:
If we divide 5760 by 681, we get 8 and a remainder of 312.
Use 8 as the next digit of our solution. 
Result so far: 518.0
The remainder is 312 after subtracting 5448 from 5760.
Bring next digit (3) of the dividend behind the 312 and repeat the process: 3123 / 681

Step 7:
681 goes into 3123 4 times with a remainder of 399.
The number 4 becomes the next digit in our result. 
Result so far: 5184.0
Subtracting 2724 from 3123 leaves us with 399.
Grab the next digit (8) from the dividend, add it to 399, then carry on: 3998 / 681

Going ahead to step 8:
681 goes into 3998 5 times with a remainder of 593.
The number 5 becomes the next digit in our result. 
Result so far: 51845.0
Deduct 3405 from 3998 and we're left with 593.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5930, and continue the process.

Step 9:
When dividing 5930 by 681, we get 8 with a remainder of 482.
Use 8 as the next digit of our solution. 
Result so far: 51845.8
Deduct 5448 from 5930 and we're left with 482.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4820, and continue the process.

Advancing to step 10:
4820 divided by 681 is 7 with a remainder of 53.
Record the quotient 7 as the next digit in the result. 
Result so far: 51845.87
If we subtract 4767 from 4820, we get 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Going ahead to step 11:
The number 681 fits into 530 0 times, leaving a remainder of 530.
Write down 0 as next digit of the result. 
Result so far: 51845.87
If we subtract 0 from 530, we get 530.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5300, and continue the process.

Going ahead to step 12:
The number 681 fits into 5300 7 times, leaving a remainder of 533.
Write down 7 as next digit of the result. 
Result so far: 51845.8707
The remainder is 533 after subtracting 4767 from 5300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5330, and continue the process.

Advancing to step 13:
If we divide 5330 by 681, we get 7 and a remainder of 563.
Use 7 as the next digit of our solution. 
Result so far: 51845.87077
If we take 4767 away from 5330, we end up with 563.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5630, and continue the process.

Our division results in 51845.87077 with a remaining 0.000563.