SOLUTION: The number 2^6• 3^2•5•7^3•11^3 is divisible by many perfect squares. How many ?

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Question 1169764: The number 2^6• 3^2•5•7^3•11^3 is divisible by many perfect squares. How many ?
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821)   (Show Source): You can put this solution on YOUR website!


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John

My calculator said it, I believe it, that settles it

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Answer by ikleyn(52824)   (Show Source): You can put this solution on YOUR website!
.

There are 4 perfect square divisors  1, 2^2, 2^4  and  2^6, associated with the prime number 2.


There are 2 perfect square divisors  1  and  3^2, associated with the prime number 3.


There are 2 perfect square divisors  1  and  7^2, associated with the prime number 7.


There are 2 perfect square divisors  1  and  11^2, associated with the prime number 11.


Combining these divisors as the factors, there are  4*2*2*2 = 4*8 = 32 divisors of the given number that are perfect squares.



ANSWER.  There are  32  (THIRTY TWO) different divisors of the given number that are perfect squares.


Solved, answered and explained.



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