document.write( "Question 1169764: The number 2^6• 3^2•5•7^3•11^3 is divisible by many perfect squares. How many ? \n" ); document.write( "

Algebra.Com's Answer #794608 by ikleyn(52855) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "There are 4 perfect square divisors  1, 2^2, 2^4  and  2^6, associated with the prime number 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There are 2 perfect square divisors  1  and  3^2, associated with the prime number 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There are 2 perfect square divisors  1  and  7^2, associated with the prime number 7.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There are 2 perfect square divisors  1  and  11^2, associated with the prime number 11.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Combining these divisors as the factors, there are  4*2*2*2 = 4*8 = 32 divisors of the given number that are perfect squares.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  There are  32  (THIRTY TWO) different divisors of the given number that are perfect squares.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );