We look at the division of 971309 by 7 
We want to divide 971309 by 7.

On to step 1:
The number 7 fits into 9 1 times, leaving a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 7 away from 9, we end up with 2.
Grab the next digit (7) from the dividend, add it to 2, then carry on: 27 / 7

On to step 2:
If we divide 27 by 7, we get 3 and a remainder of 6.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 21 away from 27, we end up with 6.
Append the next digit (1) from the dividend to 6 and continue with: 61 / 7

Moving on to step 3:
The number 7 fits into 61 8 times, leaving a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 138.0
If we take 56 away from 61, we end up with 5.
Fetch the next digit (3) from the dividend, attach it to 5 and continue: 53 / 7

Going ahead to step 4:
7 goes into 53 7 times with a remainder of 4.
Use 7 as the next digit of our solution. 
Result so far: 1387.0
Deduct 49 from 53 and we're left with 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 7

Moving on to step 5:
7 goes into 40 5 times with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 13875.0
Subtract 35 from 40 to get 5.
Fetch the next digit (9) from the dividend, attach it to 5 and continue: 59 / 7

Step 6:
If we divide 59 by 7, we get 8 and a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 138758.0
Deduct 56 from 59 and we're left 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.

Let's proceed to step 7:
7 can be fit into 30 4 times, resulting in a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 138758.4
If we subtract 28 from 30, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
7 goes into 20 2 times with a remainder of 6.
The next digit of our result is 2. 
Result so far: 138758.42
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.

Step 9:
The number 7 fits into 60 8 times, leaving a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 138758.428
Deduct 56 from 60 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 10:
The number 7 fits into 40 5 times, leaving a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 138758.4285
The remainder is 5 after subtracting 35 from 40.
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 11:
If we divide 50 by 7, we get 7 and a remainder of 1.
Use 7 as the next digit of our solution. 
Result so far: 138758.42857
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.

Let's proceed to step 12:
The number 7 fits into 10 1 times, leaving a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 138758.428571
If we subtract 7 from 10, we 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.

Going ahead to step 13:
The number 7 fits into 30 4 times, leaving a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 138758.4285714
If we take 28 away from 30, we end up 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.

Going ahead to step 14:
7 goes into 20 2 times with a remainder of 6.
The next digit of our result is 2. 
Result so far: 138758.42857142
Subtract 14 from 20 to 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.

Our division results in 138758.42857142 with a remaining 6e-09.