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 .
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 .