Here's a factor tree:

Start with 40.  Then break that down to 8 x 5, so draw two
slanted lines, one pointing to the 8 and one pointing to the 5,
like this:  

         40
         / \
        8 x 5

The 5 is prime but the 8 is not.  The 5 is at a dead end. 
We can't go any further with it. But we can break the 8 down 
as 4 x 2, so we draw two slanted lines from the 8, one 
pointing to the 4 and one to the 2, like this:

         40
         / \
        8 x 5
       / \
      4 x 2
     
The 2 is prime but the 4 is not.  The 2 is at a dead end.  
We can't go any further with it. But we can break the 4 down 
as 2 x 2, so we draw two slanted lines from the 4, one 
pointing to each of the 2's, like this:


         40
         / \
        8 x 5
       / \
      4 x 2
     / \
    2 x 2

Now everything has reached a "dead end".  
So the factor tree is complete.

So we write 40 as the product of all the 
prime numbers which occur at the "dead ends". 

40 = 2 x 2 x 2 x 5 = 23 x 5

We could also have made the factor tree, by starting 
with 40 = 10 x 4, this way:


         40
        /   \
      10  x   4
     /  \    / \ 
    2  x 5  2 x 2 

Then we end up with the same prime factorization 
just in a different order:

40 = 2 x 5 x 2 x 2 = 2 x 2 x 2 x 5 = 23 x 5.

Edwin