Question

If $F\left(n\right)$ denotes the set of all divisions of n except $1$ what is the least value of $y$ satisfying $[F\left(20\right)\cap F\left(16\right)\subseteq F\left(y\right)]$

• A. $1$
• B. $2$
• C. $4$
• D. $8$

Answer 1

The correct option is C $4$

$F\left(20\right)\cap F\left(16\right)\subseteq F\left(y\right)$
$\Rightarrow [\{2,4,5,10,20\}\cap \{2,4,8,16\}]\subseteq F\left(y\right)$
$\Rightarrow \left[\{2,4\}\right]\subseteq F\left(y\right)$
$\therefore$ The least value of $y$ is $4$.