14 divisors

Original 14 Divisors problem
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

This is the original text of the problem that has been redeveloped as Counting Factors.

The list below shows the first ten numbers together with their divisors (factors):

  1. $1$
  2. $1$, $2$
  3. $1$, $3$
  4. $1$, $2$, $4$
  5. $1$, $5$
  6. $1$, $2$, $3$, $6$
  7. $1$, $7$
  8. $1$, $2$, $4$, $8$
  9. $1$, $3$, $9$
  10. $1$, $2$, $5$, $10$

What is the smallest number with exactly twelve divisors?

What is the smallest number with exactly fourteen divisors?