Factorization tree
= Factorization tree
A <factorization tree> is a <rooted tree> whose root is an <integer> $n>1$. Each nonleaf label is a <composite number> split into two factors greater than one whose <product> equals that label; the leaves are <prime numbers>. Multiplying the leaves recovers $n$. Many <factorization trees> can have the same root, but the <fundamental theorem of arithmetic> gives them the same leaf <multiset>.