Let's divide 161 by 13
We want to figure out the number of times 161 can be divided by 13.

Let's proceed to step 1:
1 divided by 13 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 13

Advancing to step 2:
13 can be fit into 16 1 times, resulting in a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 13 from 16 to get 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 13

Let's proceed to step 3:
If we divide 31 by 13, we get 2 and a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
Deduct 26 from 31 and we're left 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.

Advancing to step 4:
13 can be fit into 50 3 times, resulting in a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 12.3
Subtract 39 from 50 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 5:
13 goes into 110 8 times with a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 12.38
Subtracting 104 from 110 leaves us 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.

Going ahead to step 6:
If we divide 60 by 13, we get 4 and a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 12.384
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 7:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 12.3846
Subtracting 78 from 80 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.

Moving on to step 8:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 12.38461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 9:
70 divided by 13 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 12.384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 10:
13 can be fit into 50 3 times, resulting in a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 12.3846153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 11:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 12.38461538
If we subtract 104 from 110, 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.

The quotient of the division is 12.38461538, and the remainder is 6e-09.