document.write( "Question 565018: You were assigned a locker for your books at school. You forgot the locker number but remmeber that two of the 12 positive factors of the locker number are 6 and 25. What is your locker number? Show or explain how you got your answer. \n" ); document.write( "

Algebra.Com's Answer #365630 by KMST(5328) $\"\"$ $\"About$

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If two of the positive factors of the number are
\n" ); document.write( " $\"6=2%2A3\"$ and $\"25=5%5E2\"$ ,
\n" ); document.write( "the number must be a multiple of $\"2%2A3%2A5%5E2=150\"$
\n" ); document.write( "The number 150 has $\"2%2A2%2A3=12\"$ positive factors.
\n" ); document.write( "Any other number who has 6 and 25 as factors will be a multiple of 150, and will have more than 12 factors.
\n" ); document.write( "So your locker is number 150.
\n" ); document.write( "How do I know $\"2%2A3%2A5%5E2=150\"$ has $\"2%2A2%2A3=12\"$ positive factors?
\n" ); document.write( "Because all the factors will be of the form
\n" ); document.write( " $\"2%5Ea%2A3%5Eb%2A5%5Ec\"$ where a and b could be 0 or 1, and c could be 0, 1, or 2.
\n" ); document.write( "That gives you 2 choices for a, 2 choices for b,and 3 choices for c. That makes $\"2%2A2%2A3=12\"$ combinations.
\n" ); document.write( "In case you don't believe, I'll list the factors of 150
\n" ); document.write( " $\"1=1%2A1%2A1=2%5E0%2A3%5E0%2A5%5E0\"$ $\"2=2%2A1%2A1=2%5E1%2A3%5E0%2A5%5E0\"$
\n" ); document.write( " $\"3=1%2A3%2A1=2%5E0%2A3%5E1%2A5%5E0\"$ $\"6=2%2A3%2A1=2%5E1%2A3%5E1%2A5%5E0\"$
\n" ); document.write( " $\"5=1%2A1%2A5=2%5E0%2A3%5E0%2A5%5E1\"$ $\"10=2%2A1%2A5=2%5E1%2A3%5E0%2A5%5E1\"$
\n" ); document.write( " $\"15=1%2A3%2A5=2%5E0%2A3%5E1%2A5%5E1\"$ $\"30=2%2A3%2A5=2%5E1%2A3%5E1%2A5%5E1\"$
\n" ); document.write( " $\"25=1%2A1%2A25=2%5E0%2A3%5E0%2A5%5E2\"$ $\"50=2%2A1%2A25=2%5E1%2A3%5E0%2A5%5E2\"$
\n" ); document.write( " $\"75=1%2A3%2A25=2%5E0%2A3%5E1%2A5%5E2\"$ $\"150=2%2A3%2A25=2%5E1%2A3%5E1%2A5%5E2\"$ \n" ); document.write( "

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