Expert: Sherry Wallin - 4/20/2010

Question
What is the largest perfect square that divides into 731808 with no remainder?

Answer
Irina~
    One way to do this problem is to prime factor 731808 and then use the largest product of each of the primes. What I am saying is:

731808
|   |
2  365904
     |  |
     2  182952
         |  |
         2  91476
             |  |
             2  45738
                 |  |
                 2  22869   here there are no more even numbers as factors and 2^5 = 32
                     |  |
                     3  7623
                          |  |
                         3 2541
                            |  |
                           3  847 at this point I know that there are no more 3"s as factors
                               |  |
                             7  121
                                 |  |
                                11 11

The prime factorization is 2^5*3^3*7*11^2 which is equivalent to 2^4*2*3^2*3*7*11^2. Now take any factor that has an even number exponent and use it in your largest perfect square: 2^4*3^2*11^2 = 17424 = 132^2

So 17424 is the largest perfect square that divided 731808

Math Prof