971971 ÷ 13 
We want to figure out the number of times 971971 can be divided by 13.

Going ahead to step 1:
If we divide 9 by 13, we get 0 and a remainder of 9.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Fetch the next digit (7) from the dividend, attach it to 9 and continue: 97 / 13

On to step 2:
97 divided by 13 is 7 with a remainder of 6.
The next digit of our result is 7. 
Result so far: 7.0
If we take 91 away from 97, we end up with 6.
Include the next digit (1) from the dividend after 6, then repeat: 61 / 13

On to step 3:
When dividing 61 by 13, we get 4 with a remainder of 9.
The number 4 becomes the next digit in our result. 
Result so far: 74.0
The remainder is 9 after subtracting 52 from 61.
Grab the next digit (9) from the dividend, add it to 9, then carry on: 99 / 13

On to step 4:
13 goes into 99 7 times with a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 747.0
If we subtract 91 from 99, we get 8.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 13

Going ahead to step 5:
13 can be fit into 87 6 times, resulting in a remainder of 9.
Put 6 as the next digit of the answer. 
Result so far: 7476.0
Subtract 78 from 87 to get 9.
Take the next digit (1) from the dividend and append it to 9, then repeat: 91 / 13

Moving on to step 6:
The number 13 fits into 91 7 times, leaving a remainder of 0.
Write down 7 as next digit of the result. 
Result so far: 74767.0
Deduct 91 from 91 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 7:
13 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 74767.0
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 8:
When dividing 0 by 13, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 74767.0
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 74767.0, with a leftover of 0.0.