35814 ÷ 7 
Our goal is to divide 35814 by 7.

On to step 1:
When dividing 3 by 7, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 7

On to step 2:
When dividing 35 by 7, we get 5 with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 35 from 35, we get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 7

On to step 3:
8 divided by 7 is 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 51.0
The remainder is 1 after subtracting 7 from 8.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 7

On to step 4:
If we divide 11 by 7, we get 1 and a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 511.0
Deduct 7 from 11 and we're left with 4.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 7

Going ahead to step 5:
7 goes into 44 6 times with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 5116.0
The remainder is 2 after subtracting 42 from 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 6:
7 goes into 20 2 times with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 5116.2
The remainder is 6 after subtracting 14 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 7:
The number 7 fits into 60 8 times, leaving a remainder of 4.
The next digit of our result is 8. 
Result so far: 5116.28
If we subtract 56 from 60, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
7 goes into 40 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 5116.285
If we subtract 35 from 40, 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.

Step 9:
If we divide 50 by 7, we get 7 and a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 5116.2857
Subtract 49 from 50 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 10:
7 can be fit into 10 1 times, resulting in a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 5116.28571
Subtract 7 from 10 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 11:
The number 7 fits into 30 4 times, leaving a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 5116.285714
The remainder is 2 after subtracting 28 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 12:
The number 7 fits into 20 2 times, leaving a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 5116.2857142
If we take 14 away from 20, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 13:
60 divided by 7 is 8 with a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 5116.28571428
The remainder is 4 after subtracting 56 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 5116.28571428, and the remainder is 4e-09.