document.write( "Question 1132327: which numbers that are less than 100 have the most factors? How many different prime factors do these numbers have? \n" ); document.write( "
Algebra.Com's Answer #749335 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "I'd reformulate this problem in this way\r
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document.write( "    What are the numbers that are less than 100 and have maximal number of \"highlight%28cross%28factors%29%29\" divisors? \r\n" );
document.write( "    How many different prime \"highlight%28cross%28factors%29%29\" divisors do these numbers have?\r\n" );
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\n" ); document.write( "to make the formulation more precise (and more professional).\r
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document.write( "The number  96 = \"2%5E5%2A3\"  has  (1+5)*(1+1) = 6*2 = 12 divisors  \r\n" );
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document.write( "    1, 2,  4,  8, 16, 32,\r\n" );
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document.write( "    3, 6, 12, 24, 48, 96.\r\n" );
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document.write( "It has two prime divisors  2  and  3.\r\n" );
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document.write( "The number  60 = \"2%5E2%2A3%2A5\"  has  (1+2)*(1+1)*(1+1) = 3*2*2 = 12 divisors  \r\n" );
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document.write( "    1,   2,   4, \r\n" );
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document.write( "    3,   6,  12,\r\n" );
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document.write( "    5,  10,  20,\r\n" );
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document.write( "    15, 30,  60.\r\n" );
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document.write( "It has three prime divisors  2, 3 and 5.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I didn't check that these numbers provide the maximum number of divisors, but I think it is so.\r
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\n" ); document.write( "\n" ); document.write( "Having this  HINT  from me,  you may check/(or disprove) it on your own.\r
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\n" ); document.write( "\n" ); document.write( "Addition : \r
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\n" ); document.write( "\n" ); document.write( "        1)   I was right with the numbers 60 and 96.\r
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\n" ); document.write( "\n" ); document.write( "        2)   The numbers  84  and  90  also have  12  divisors each.\r
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\n" ); document.write( "\n" ); document.write( "        See the table of divisors in this Wikipedia article\r
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document.write( "        https://en.wikipedia.org/wiki/Table_of_divisors#1_to_100\r\n" );
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