13222541 ÷ 971 
Our goal is to divide 13222541 by 971.

Advancing to step 1:
971 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 971

On to step 2:
When dividing 13 by 971, we get 0 with a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 13, we end up with 13.
Bring next digit (2) of the dividend behind the 13 and repeat the process: 132 / 971

Step 3:
The number 971 fits into 132 0 times, leaving a remainder of 132.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 132 leaves us with 132.
Take the next digit (2) from the dividend and append it to 132, then repeat: 1322 / 971

Advancing to step 4:
The number 971 fits into 1322 1 times, leaving a remainder of 351.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 971 away from 1322, we end up with 351.
Take the next digit (2) from the dividend and append it to 351, then repeat: 3512 / 971

Let's proceed to step 5:
971 can be fit into 3512 3 times, resulting in a remainder of 599.
Put 3 as the next digit of the answer. 
Result so far: 13.0
If we subtract 2913 from 3512, we get 599.
Append the next digit (5) from the dividend to 599 and continue with: 5995 / 971

Advancing to step 6:
When dividing 5995 by 971, we get 6 with a remainder of 169.
Record the quotient 6 as the next digit in the result. 
Result so far: 136.0
Subtract 5826 from 5995 to get 169.
Take the next digit (4) from the dividend and append it to 169, then repeat: 1694 / 971

On to step 7:
If we divide 1694 by 971, we get 1 and a remainder of 723.
The next digit of our result is 1. 
Result so far: 1361.0
Subtract 971 from 1694 to get 723.
Include the next digit (1) from the dividend after 723, then repeat: 7231 / 971

Moving on to step 8:
971 can be fit into 7231 7 times, resulting in a remainder of 434.
Record the quotient 7 as the next digit in the result. 
Result so far: 13617.0
The remainder is 434 after subtracting 6797 from 7231.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4340, and continue the process.

Let's proceed to step 9:
971 can be fit into 4340 4 times, resulting in a remainder of 456.
The next digit of our result is 4. 
Result so far: 13617.4
Subtracting 3884 from 4340 leaves us with 456.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4560, and continue the process.

Let's proceed to step 10:
If we divide 4560 by 971, we get 4 and a remainder of 676.
Put 4 as the next digit of the answer. 
Result so far: 13617.44
If we take 3884 away from 4560, we end up with 676.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6760, and continue the process.

The quotient of the division is 13617.44, and the remainder is 0.676.