document.write( "Question 1175732: How many positive integer factors of 360 are also multiples of 4? \n" ); document.write( "

Algebra.Com's Answer #801412 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The solution by @MathLover1 is incorrect.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            Her answer \" 14 \" is not correct.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The numbers 16 and 32 of her list are not divisors of 360.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            I came to bring the correct solution.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "360 = 4*90 = 8*45 = 8*3^2*5 = 4*(2*3^2*5).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "All divisors of 360, that are multiples of 4, are the numbers of the primary decomposition  ,\r\n" );
document.write( "\r\n" );
document.write( "where indexes m, n and k  vary independently in their ranges\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    m = 0, 1     (two values)\r\n" );
document.write( "\r\n" );
document.write( "    n = 0, 1, 2  (three values)\r\n" );
document.write( "\r\n" );
document.write( "    k = 0, 1     (two values).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "THEREFORE, the number of all positive divisors of 360, that are multiples of 4 is  2*3*2 = 12.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you want to learn on how to calculate the number of divisors d(N) of a given integer number N, look into my lesson\r
\n" ); document.write( "\n" ); document.write( " - Problems on divisors of a given number \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is one of the basic introductory subjects of the elementary number theory.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );