Question 33101
built it up gradually:


704 is
2*352
2*2*176
2*2*2*88
2*2*2*2*44
2*2*2*2*2*22
2*2*2*2*2*2*11


this is as far as you can go, since 2 and 11 are both primes.



Looking at the set of 2's... 
2*2*2*2*2*2 is 64


so we have 64*11


64 is the largest perfect square factor (since {{{8^2}}} is 64).


jon.