document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201254>Question 1201254</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the total number of divisors of the number 5880. How many are even? How many are odd? </SPAN>\n" );
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document.write( "Find the prime factorization....<br><BR>\n" );
document.write( "5880<BR>\n" );
document.write( "588*10<BR>\n" );
document.write( "4*147*2*5<BR>\n" );
document.write( "2*2*7*21*2*5<BR>\n" );
document.write( "2*2*7*7*3*2*5<br><BR>\n" );
document.write( "The prime factorization is (2^3)(3^1)(5^1)(7^2).<br><BR>\n" );
document.write( "To find the total number of divisors, add 1 to each of the exponents in the prime factorization and multiply those numbers.  The total number of divisors is 4*2*2*3 = 48.<br><BR>\n" );
document.write( "The odd divisors are those that do not contain any factor of 2.  To find the number of odd divisors, add 1 to each of the exponents of an odd prime factor and multiply those numbers.  The number of odd divisors is 2*2*3 = 12.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "total number of divisors: 48<BR>\n" );
document.write( "number of odd divisors: 12<BR>\n" );
document.write( "number of even divisors: 48-12 = 36<br><BR>\n" );
document.write( " </SPAN>\n" );
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