Question

The number $4$ is the smallest positive integer that has exactly three factors: $1,2$ and $4$. If $k$ is the smallest positive integer after $4$ to have exactly three factors, then find the sum of the three factors of $k$

• A. $13$
• B. $14$
• C. $16$
• D. $18$
• E. $20$

Answer 1

The correct option is A $13$

Smallest positive integer after $4$ that has exactly three factors is $9$ because

Factor of $5=1,4$

Factor of $6=1,2,3,6$

Factor of $7=1,7$

Factor of $8=1,2,4,8$

Factor of $9=1,3,9$

So the value of $k$ is $9$.

$\therefore$Sum of factors$=1+3+9=13$