2021 April MIMC 10 Problems/Problem 20
Given that . Given that the product of the even divisors is
, and the product of the odd divisors is
. Find
.
Solution
We can prime factorize the number first. . All of the odd factors of
would be factors of
. Therefore, there are
odd factors of
. Let those factors form a set
, and all even factors would be
(all elements in
multiplied by
),
,
,
. Let the product of all odd factors in
be
, then the product of all even factors would be
. Therefore, the ratio of
.