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?
+491 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
So
(m + 1) ( n + 1) = 20
And m, n could be (in some order)
3, 4 or
1, 9
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
So
(k + 1) (m + 1) ( n + 1) = 20
And k, m, n could be (in some order)
1, 1, 4
Credit to CPhill for answer
