Question 1063715
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I kept dividing by 2 until I got an odd number:

8124287104÷2 = 4062143662 
4062143552÷2 = 2031071776
2031071776÷2 = 1015535888
1015535888÷2 =  507767944
 507767944÷2 =  253883972
 253883972÷2 =  126941986
 126941986÷2 =   63470993  <--an odd number

So 8124287104 = 2<sup>7</sup>&#8729;63470993

We know that 2<sup>6</sup> = (2<sup>3</sup>)<sup>2</sup> = 8<sup>2</sup> = 64

is a perfect square that divides 8124287104.

But we don't know if there is a larger one.  So I went to

http://compoasso.free.fr/primelistweb/page/prime/liste_online_en.php

and typed in 63470993 to see if it is prime and found that it was not.

So I tried dividing it by primes 3,5,7,11,13,17,19,23,29,31,37,41

and found that 63470993 = 41&#8729;1548073

I went to that site again and found that 1548073 is indeed a prime.

So 64 is the largest perfect square that divides 8124287104.

64 has two square roots, which are 8 and -8.

Edwin</pre>