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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?