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?

Can you find any patterns?

How did you go about solving this problem?