What does prime-to-p-part mean?

Question

What does prime-to-p-part mean ?

Answer 1

If $p^a$ exactly divides $e$ (i.e., $p^a$ divides $e$ but $p^{a+1}$ does not; written $p^a \mid\mid e$ ),

then the prime-to-$p$ part of $e$ is $e/p^a$.