We look at the division of 137827 by 13 
Our goal is to divide 137827 by 13.

Let's proceed to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 13

Moving on to step 2:
The number 13 fits into 13 1 times, leaving a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 13 away from 13, we end up with 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 13

Going ahead to step 3:
13 can be fit into 7 0 times, resulting in a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
If we subtract 0 from 7, we get 7.
Fetch the next digit (8) from the dividend, attach it to 7 and continue: 78 / 13

Step 4:
The number 13 fits into 78 6 times, leaving a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 106.0
Subtract 78 from 78 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 13

Moving on to step 5:
The number 13 fits into 2 0 times, leaving a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 1060.0
If we subtract 0 from 2, we get 2.
Take the next digit (7) from the dividend and append it to 2, then repeat: 27 / 13

On to step 6:
13 goes into 27 2 times with a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 10602.0
Subtracting 26 from 27 leaves us 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.

Moving on to step 7:
The number 13 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 10602.0
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
100 divided by 13 is 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 10602.07
If we take 91 away from 100, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 9:
If we divide 90 by 13, we get 6 and a remainder of 12.
The next digit of our result is 6. 
Result so far: 10602.076
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 10:
120 divided by 13 is 9 with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 10602.0769
If we take 117 away from 120, 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.

On to step 11:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 10602.07692
Subtracting 26 from 30 leaves us 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.

Advancing to step 12:
If we divide 40 by 13, we get 3 and a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 10602.076923
If we take 39 away from 40, 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.

Advancing to step 13:
13 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 10602.076923
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 14:
13 goes into 100 7 times with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 10602.07692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

The final outcome is 10602.07692307, with a leftover of 9e-09.