The factors of x include 2, 4, 9. Which of the following are also factors of x?
{1, 3, 5, 6, 8, 10, 12, 18, 24, 36}
Apparently the correct answer is {1, 3, 6, 12, 18, and 36} but I have trouble seeing how 36 is a factor and 24 is not. Whats the best method for finding which numbers in the set are factors.
Also since 2 is already a factor of 4 does the extra 2 they provide count as a distinct factor of x or could in be included in the 4? As in, if they said the factors were 4 and 9 would that be a different problem?
If $4$ is a factor of $x$, then by extension $2$ is a factor because $4=2^2$. Every number has $1$ as a factor as well, so we can guarantee that the factors of $x$ include $1$, $2^2$, and $3^2$.
If the product of all of these is a factor of $x$, then we can say that the product of any subset will also be a factor of $x$.
This means that we can say that the other factors of $x$ include $2^2\cdot3^2$, $2^2\cdot3$, $2\cdot3^2$, and $2\cdot3$.