Building the Factor Tree
So let's go through the process of creating the factor tree for the number 24. To start, write down 24 on a piece of paper (leave plenty of room on either side) and circle it. The circle shows that this is actually the node of a tree; lines between nodes will are called edges of the tree.
The first prime number is two. Two divides evenly into 24 (that is, 24 divided by 2 has no remainder), so write two underneath 24 and to the left. 24 divided by 2 is 12, so write 12 to the right of the two. Circle both numbers and draw an edge from each new circle up to the circle containing the 24. Your drawing should look like the top section of the picture at right.
Now, we go down to the 12. Twelve is also divisible by two, so we put another two underneath it, along with a six, which is the quotient of twelve and two. Six is also divisible by two, so underneath the six we put a two and a three.
Three is not divisible by two, which means we need to try the next prime number. The smallest prime number after two is three; in other words, the current value is already prime, so we're done. Since the current node (each circled number is called a node of the tree) is prime, every leaf (a node with no children, that is, no nodes hanging from it) of the tree is prime, and we are done. By reading off all the leaves, we can see that 24 = 2 x 2 x 2 x 3.