The n! (read n factorial) function give the product of the integers 1
33! = 1 · 2 · 3 ···
31 · 32 · 33 = 8,683,317,618,811,886,495,518,194,401,280,000,000.
Finding perfect square divisors of this 37 digit number seems like an impossible amount of
work, but finding the number of these factors is fairly easy using nothing harder
than prime factoring, and you don't need to directly factor the huge number. Start by thinking
about the prime factorizatiion of n! .