document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179657>Question 179657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Based on my previous questions and the answer provided:<BR>\n" );
document.write( "``Hello I have a question regarding the easiest way to find the positive divisors of a number. I know there is a way to find them in a quick way instead of going through every number. For example I have this number 372. and even though I got the answer, it willtake me for ever to come up with 1,2,3,4,6,12,32,62,93,124,186,372. Please can you explain me how can I find the positive divisors more effectively? \"\r<BR>\n" );
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document.write( "Answer: \"You just have to obtain the prime factor decomposition of the number and then to combine those factors in all possible forms. <BR>\n" );
document.write( "If they only ask you only by the NUMBER of divisors, that's a lot easier. It's only a problem of counting. For example: <BR>\n" );
document.write( "756 = (3^3) * (2^2) * 7 <BR>\n" );
document.write( "Any factor you may have will be a combination (product) of these factors. You have available 3 \"3\"s, 2 \"2\"s and 1 \"7\", so <BR>\n" );
document.write( "# of ways factor \"3\" may appear = 3 + 1 = 4 (3^0, 3^1, 3^2, 3^3)<BR>\n" );
document.write( "# of ways factor \"2\" may appear = 2 + 1 = 3 (2^0, 2^1, 2^2)<BR>\n" );
document.write( "# of ways factor \"7\" may appear = 1 + 1 = 2 (7^0, 7^1) <BR>\n" );
document.write( "thus: # of ways these factors may be combined = 4*3*2 = 24 <BR>\n" );
document.write( "=> there are 24 factors \r<BR>\n" );
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document.write( "I HAVE ANOTHER QUESTION\r<BR>\n" );
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document.write( "I think i got a little lost. I got the last part, but how did you figure out that 756 = 3^3 *2^2 *7? Where did you get the numbers from. And also one last question, I would know that there are 24 numbers, but how would i know which ones will be the divisors? <BR>\n" );
document.write( "And thanks again </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134580 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=134580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 756=2*2*3*3*3*7<BR>\n" );
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document.write( "start with a known prime factor such as 2(since this is and even number) and then factor out all the primes.<BR>\n" );
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document.write( "If you know rules of divisibility use those.The digits of this number 7+5+6=18 which is divisible by 9 so we know this number is divisible by 9. <BR>\n" );
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document.write( "and just keep working it down with as big of numbers as you can. </SPAN>\n" );
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