document.write( "Question 1210186: Find the number of positive integers that are divisors of at least one of 6^{6}, 10^{10}, 15^{15}, and 30^{30}.
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Algebra.Com's Answer #851543 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Notice that all three numbers  ,    and    are divisors of the number  .\r\n" );
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document.write( "Therefore, you can simplify the problem's formulation: you ONLY need to find the number of divisors of  .\r\n" );
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document.write( "The prime decomposition for 30 is  30 = 2*3*5.\r\n" );
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document.write( "So,   = .\r\n" );
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document.write( "For this number, its divisors are all  \r\n" );
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document.write( "    1,  2,  , . . . ,     (31 divisor),\r\n" );
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document.write( "    1,  3,  , . . . ,     (31 divisor),\r\n" );
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document.write( "    1,  5,  , . . . ,     (31 divisor)\r\n" );
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document.write( "and all of their products.\r\n" );
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document.write( "The number of all their distinct products is  31*31*31 =  = 29791.\r\n" );
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document.write( "It is the ANSWER to the problem's question.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "I wrote this my post after @CPhill to provide the most simple straightforward solution/explanation
\n" ); document.write( "and to remove all unnecessary complications from the post by @CPhill.\r
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\n" ); document.write( "\n" ); document.write( "Edwin, I think it was very good from your side to make this editing in your post
\n" ); document.write( "and to exclude/ (to remove) your unjustified insinuations against me from the original version.\r
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