208442 ÷ 15 
We're looking to find how many times 15 goes into 208442.

Let's proceed to step 1:
When dividing 2 by 15, we get 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 15

Advancing to step 2:
When dividing 20 by 15, we get 1 with a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 15 from 20, we get 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 15

Advancing to step 3:
15 goes into 58 3 times with a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
If we subtract 45 from 58, we get 13.
Bring next digit (4) of the dividend behind the 13 and repeat the process: 134 / 15

Moving on to step 4:
When dividing 134 by 15, we get 8 with a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 138.0
If we subtract 120 from 134, we get 14.
Include the next digit (4) from the dividend after 14, then repeat: 144 / 15

On to step 5:
15 can be fit into 144 9 times, resulting in a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 1389.0
If we subtract 135 from 144, we get 9.
Grab the next digit (2) from the dividend, add it to 9, then carry on: 92 / 15

On to step 6:
15 goes into 92 6 times with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 13896.0
Deduct 90 from 92 and we're left 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.

Advancing to step 7:
15 goes into 20 1 times with a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 13896.1
Subtract 15 from 20 to get 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 8:
50 divided by 15 is 3 with a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 13896.13
Subtracting 45 from 50 leaves us 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.

Let's proceed to step 9:
15 can be fit into 50 3 times, resulting in a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 13896.133
If we subtract 45 from 50, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

After the division, we end up with 13896.133 and a remainder of 0.0005.