Find the smallest positive integer such that it has exactly 100 different positive integer divisors including 1 and the number itself.
100 = 22 × 52 = 2 × 2 × 5 × 5 = (1 + 1) (1 + 1) (4 + 1) (4 + 1)
N =P14 P24P31P41
N = 24345171 = 45, 360.
