Which one of these is prime of $3\Bbb Z$?
$42\Bbb Z$,$24\Bbb Z$,$12\Bbb Z$,$9\Bbb Z$ and $33\Bbb Z$
I tried to check their factor groups if they are integral domains. because
An ideal I in a ring R is a prime ideal if the quotient ring R/I is an integral domain.
$3\Bbb Z/42\Bbb Z\cong\Bbb Z/14\Bbb Z\cong\Bbb Z_{14}$ not an integral domain so not a prime ideal.
Is this approach wrong?