We look at the division of 186506 by 13 
We're looking to find how many times 13 goes into 186506.

Advancing to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (8) from the dividend, attach it to 1 and continue: 18 / 13

Let's proceed to step 2:
The number 13 fits into 18 1 times, leaving a remainder of 5.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 13 from 18 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 13

Advancing to step 3:
13 can be fit into 56 4 times, resulting in a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 14.0
If we subtract 52 from 56, we get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 13

On to step 4:
13 can be fit into 45 3 times, resulting in a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 143.0
Subtracting 39 from 45 leaves us with 6.
Append the next digit (0) from the dividend to 6 and continue with: 60 / 13

Advancing to step 5:
If we divide 60 by 13, we get 4 and a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 1434.0
Subtracting 52 from 60 leaves us with 8.
Grab the next digit (6) from the dividend, add it to 8, then carry on: 86 / 13

Going ahead to step 6:
86 divided by 13 is 6 with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 14346.0
Subtract 78 from 86 to 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.

Moving on to step 7:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 14346.6
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
When dividing 20 by 13, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 14346.61
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 9:
When dividing 70 by 13, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 14346.615
Deduct 65 from 70 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.

Moving on to step 10:
50 divided by 13 is 3 with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 14346.6153
If we subtract 39 from 50, we 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.

Step 11:
110 divided by 13 is 8 with a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 14346.61538
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.

Moving on to step 12:
When dividing 60 by 13, we get 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 14346.615384
Subtract 52 from 60 to 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.

Advancing to step 13:
80 divided by 13 is 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 14346.6153846
If we take 78 away from 80, we end up 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 14:
13 goes into 20 1 times with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 14346.61538461
If we take 13 away from 20, we end up 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.

After the division, we end up with 14346.61538461 and a remainder of 7e-09.