A set $S$ of whole numbers is called stapled if and only if for every whole number $a$ which is in $S$ there exists a prime factor of $a$ which divides at least one other number in $S$.
Let $T$ be a set of whole numbers. Which of the following is true if and only if $T$ is not stapled?
A For every number $a$ which is in $T$, there is no prime factor of $a$ which divides every other number in $T$.
B For every number $a$ which is in $T$, there is no prime factor of $a$ which divides at least one other number in $T$.
C For every number $a$ which is in $T$, there is a prime factor of $a$ which does not divide any other number in $T$.
D For every number $a$ which is in $T$, there is a prime factor of $a$ which does not divide at least one other number in $T$.
E There exists a number $a$ which is in $T$ such that there is no prime factor of $a$ which divides every other number in $T$.
F There exists a number $a$ which is in $T$ such that there is no prime factor of $a$ which divides at least one other number in $T$.
G There exists a number $a$ which is in $T$ such that there is a prime factor of $a$ which does not divide any other number in $T$.
H There exists a number $a$ which is in $T$ such that there is a prime factor of $a$ which does not divide at least one other number in $T$.