Smallest Number with 28 Positive Divisors

[ehrenfest]

Homework Statement

Find the smallest number with 28 positive divisors.

28 = 14*2 or 7*4.

So, it is either 2^13*3 or 2^6*3^3, right?

Because 2^7 is manifestly larger than 3^2, it the latter, correct?

Homework Equations

The Attempt at a Solution

 

[morphism]

Sounds good to me.