Decompose into prime factors the integers 2, 4, 6, 9, 17, 72.
$2=2^{1}, 4=2^{2}, 6=2 \times 3, 9=3^{2}, 17=17^{1}, 72=2^{3} \times 3^{2}$. To decompose an integer into prime factors $n$, we look for a prime divisor $p$ of $n$ (for example, the smallest divisor of $n$), and we decompose $\frac{n}{p}$ into prime factors.

Definition 12. For a strictly positive integer $n$, and a prime number $p$, we denote $\nu_{p}(n)$ the greatest integer $k$ such that $p^{k}$ divides $n$. This is also the exponent of $p$ in the prime factorization.