Question

If the set of factors of a whole number $n$, including $n$ itself but not $1$ is denoted by $F\left(n\right),$ and $F\left(16\right)\cap F\left(40\right)$ = $F\left(x\right)$ then $x$ is

• A. 4
• B. 8
• C. 6
• D. 10

Answer 1

The correct option is B

8

From the given definition that \(F(n)\) is the set of factors of a whole number $n$, including $n$ itself but not $1$.
We can compute
$F\left(16\right)=\{2,4,8,16\}$

and
$F\left(40\right)=\{2,4,5,8,10,20,40\}$

Also
$F\left(16\right)\cap F\left(40\right)=F\left(x\right)[\because \text{given}]$
$\Rightarrow \{2,4,8\}=F\left(x\right)$

$\Rightarrow F\left(8\right)=F\left(x\right)$
⟹$x=8$