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?

Guest Feb 3, 2021

#1**0 **

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

Elijah Feb 3, 2021