13627 divided by 12 
We want to figure out the number of times 13627 can be divided by 12.

On to step 1:
If we divide 1 by 12, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 12

Moving on to step 2:
13 divided by 12 is 1 with a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 12 away from 13, we end up with 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 12

On to step 3:
12 can be fit into 16 1 times, resulting in a remainder of 4.
The next digit of our result is 1. 
Result so far: 11.0
Subtracting 12 from 16 leaves us with 4.
Include the next digit (2) from the dividend after 4, then repeat: 42 / 12

Advancing to step 4:
When dividing 42 by 12, we get 3 with a remainder of 6.
Record the quotient 3 as the next digit in the result. 
Result so far: 113.0
Deduct 36 from 42 and we're left with 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 12

Going ahead to step 5:
67 divided by 12 is 5 with a remainder of 7.
Record the quotient 5 as the next digit in the result. 
Result so far: 1135.0
Deduct 60 from 67 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 6:
12 can be fit into 70 5 times, resulting in a remainder of 10.
The next digit of our result is 5. 
Result so far: 1135.5
Deduct 60 from 70 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.

Let's proceed to step 7:
If we divide 100 by 12, we get 8 and a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 1135.58
Subtract 96 from 100 to get 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 8:
If we divide 40 by 12, we get 3 and a remainder of 4.
Record the quotient 3 as the next digit in the result. 
Result so far: 1135.583
Subtracting 36 from 40 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.

Let's proceed to step 9:
If we divide 40 by 12, we get 3 and a remainder of 4.
Put 3 as the next digit of the answer. 
Result so far: 1135.5833
Deduct 36 from 40 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.

The quotient of the division is 1135.5833, and the remainder is 4e-05.