706557 ÷ 7 
Our goal is to divide 706557 by 7.

Moving on to step 1:
7 can be fit into 7 1 times, resulting in a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 7 from 7 to get 0.
Fetch the next digit (0) from the dividend, attach it to 0 and continue: 0 / 7

Advancing to step 2:
If we divide 0 by 7, we get 0 and a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 10.0
Deduct 0 from 0 and we're left with 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 7

Let's proceed to step 3:
If we divide 6 by 7, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 100.0
Subtracting 0 from 6 leaves us with 6.
Include the next digit (5) from the dividend after 6, then repeat: 65 / 7

Let's proceed to step 4:
7 can be fit into 65 9 times, resulting in a remainder of 2.
The next digit of our result is 9. 
Result so far: 1009.0
If we take 63 away from 65, we end up with 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 7

Step 5:
The number 7 fits into 25 3 times, leaving a remainder of 4.
The next digit of our result is 3. 
Result so far: 10093.0
If we subtract 21 from 25, we get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 7

On to step 6:
7 goes into 47 6 times with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 100936.0
The remainder is 5 after subtracting 42 from 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 7:
7 goes into 50 7 times with a remainder of 1.
The next digit of our result is 7. 
Result so far: 100936.7
If we take 49 away from 50, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 8:
When dividing 10 by 7, we get 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 100936.71
The remainder is 3 after subtracting 7 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 9:
When dividing 30 by 7, we get 4 with a remainder of 2.
The next digit of our result is 4. 
Result so far: 100936.714
Subtracting 28 from 30 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 10:
When dividing 20 by 7, we get 2 with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 100936.7142
If we subtract 14 from 20, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 11:
If we divide 60 by 7, we get 8 and a remainder of 4.
The next digit of our result is 8. 
Result so far: 100936.71428
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.

Advancing to step 12:
The number 7 fits into 40 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 100936.714285
Subtracting 35 from 40 leaves us with 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 13:
The number 7 fits into 50 7 times, leaving a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 100936.7142857
Deduct 49 from 50 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 14:
If we divide 10 by 7, we get 1 and a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 100936.71428571
If we take 7 away from 10, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Our division results in 100936.71428571 with a remaining 3e-09.