though I don't fully understand at what size number these modules become necessary
*Much* smaller numbers than the ones you're dealing
with. The details are platform-dependent; for
instance, a 64-bit platform can handle, without
a big-number library, larger numbers than a 32-bit
platform. But nobody is ever going to manufacture
a computer that can natively handle numbers of the
size you're talking about. Based on Moore's law,
you couldn't expect such a computer to be available
while Earth is still inhabitable.
You may want to look into ways to approximate
factorials. Irrespective of what number library you
use, I'm not sure it's possible to calculate
the exact value of the factorial of 700 in reasonable
time on a household computer.
Alternatively, look for ways to shortcut the problem,
by simplifying before you multiply. You may find
that some things cancel out in ways that save a lot
of time. Also, if this is for a math class, you
may want to check, as some math teachers are quite
happy to receive answers in expression form, with
not all of the calculations performed, because they're
more interested in whether you understand how to work
the problem than in whether you can multiply together
a few hundred numbers.
"In adjectives, with the addition of inflectional endings, a changeable long vowel (Qamets or Tsere) in an open, propretonic syllable will reduce to Vocal Shewa. This type of change occurs when the open, pretonic syllable of the masculine singular adjective becomes propretonic with the addition of inflectional endings."
— Pratico & Van Pelt, BBHG, p68