What is the maximum possible length of an integer less than 600? (the length of an integer is the total number of prime

[BTGmoderatorDC]

What is the maximum possible length of an integer less than 600?
(the length of an integer is the total number of prime factors in its prime factorization)

A) 6
B) 7
C) 8
D) 9
E) 10


OA D

Source: Manhattan Prep

[Ian Stewart]

We'll get the "longest" number by multiplying the smallest primes together -- in other words, we want to use as many 2's as we can. Since 2^9 = 512 is less than 600, but 2^10 is greater than 600, the answer is 9.