A certain positive integer has exactly 20 positive divisors.
What is the smallest possible value of the number?
What is the largeest possible value of the number?
This has been asked before
a) We could have two primes that divide the integer
Suppose that the number can be prime-factored into a^m * b^n
(m + 1) ( n + 1) = 20
And m, n could be (in some order)
3, 4 or
b ) We could have three primes that divide the integer
Suppose that the integer can be prime-factored into a^k * b *m * c ^n
(k + 1) (m + 1) ( n + 1) = 20
And k, m, n could be (in some order)
1, 1, 4
Credit to CPhill for answer