Question

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

• A. $1$
• B. $2$
• C. $4$
• D. $8$

Answer 1

The correct option is C

$4$

Finding the least value$y$:

Given, $F\left(n\right)$ denotes the set of all divisors of n except $1,$

$F\left(20\right)=\left\{2,4,5,10,20\right\}$

$F\left(16\right)=\left\{2,4,8,16\right\}$

$\Rightarrow$$F\left(20\right)\cap F\left(16\right)=\left\{2,4\right\}$

According to question $F\left(y\right)=\left\{2,4\right\}$

Least value of $y=4$.

Hence, correct answer is option $\left(C\right)$