document.write( "Question 1119665: What is the smallest positive integer that has exactly: 6 divisors \n" ); document.write( "

Algebra.Com's Answer #735277 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Answer. The smallest positive integer that has exactly 6 divisors is 12 = $\"2%5E2%2A3\"$ .\r
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document.write( "1.  For integer number N = ,  where p is a prime number and  is an integer exponent (index), \r\n" );
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document.write( "    You can easily check it:  the divisors  are  1, p, , . . . , .\r\n" );
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document.write( "2.  For integer number  N = ,  where p, q, . . . , r are prime divisors and , , . . . ,  are integer exponents (indexes)  \r\n" );
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document.write( "    the number of divisors is  .\r\n" );
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document.write( "3.  From these facts, you can easily obtain the answer.\r\n" );
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document.write( "    Notice that  6 = 2*3.\r\n" );
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document.write( "    It is easy to list those divisors:  1, 2, 4, 3, 6, 12.\r\n" );
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