Question

How do you write the factor trees for 24?

Answer 1

Keep "breaking off" prime pieces until you can't do it anymore.

Explanation:

`"       24"`               24 is even; we can take out a factor of 2.
`"      /  \"`
`"     2   12"`            12 is also even; take out another 2.
`"         /  \"`
`"        2    6"`         6 is again even, so we take out another 2.
`"            /  \"`
`"           2    3"`      3 is prime. We are done.

The prime factorization of `24` is the product of all the "nodes" of the tree. In this case,

`24=2times2times2times3`, or
`24=2^3times3`

The final factor tree can be written as above, or it can be written with all the nodes carried down to the bottom line:

`"       24"`
`"      /  \"`
`"     2   12"`
`"    /   /  \"`
`"   2   2    6"`
`"  /   /    / \"`
`" 2   2    2   3"`

This takes more time, but it is easier to find all the nodes, because they're all on the bottom row.