We look at the division of 15937 by 3 
We want to figure out the number of times 15937 can be divided by 3.

Moving on to step 1:
The number 3 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Take the next digit (5) from the dividend and append it to 1, then repeat: 15 / 3

Advancing to step 2:
3 can be fit into 15 5 times, resulting in a remainder of 0.
The next digit of our result is 5. 
Result so far: 5.0
Deduct 15 from 15 and we're left with 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 3

Advancing to step 3:
9 divided by 3 is 3 with a remainder of 0.
The next digit of our result is 3. 
Result so far: 53.0
Subtract 9 from 9 to get 0.
Append the next digit (3) from the dividend to 0 and continue with: 3 / 3

Moving on to step 4:
3 goes into 3 1 times with a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 531.0
If we take 3 away from 3, we end up with 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 3

Let's proceed to step 5:
The number 3 fits into 7 2 times, leaving a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 5312.0
Subtract 6 from 7 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 6:
3 goes into 10 3 times with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 5312.3
Subtracting 9 from 10 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.

Advancing to step 7:
If we divide 10 by 3, we get 3 and a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 5312.33
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final outcome is 5312.33, with a leftover of 0.001.