Problem of the Week 30

Twelve is the least positive integer with six different positive factors.  The factors are 1, 2, 3, 4, 6, and 12.  What is the least positive integer with exactly twenty-four different positive factors?

 

Alternate Problem 30

The numbers in the sequence 2, 7, 12, 17, 22, 27, 32, 37, … increase by 5s.  The numbers in the sequence 3, 10, 17, 24, 31, 38, 45, 52, … increase by 7s.  What are the first ten numbers that appear in both sequences?

 

Extension Problem 30

What is the least natural number that has exactly 100 natural factors?