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Homework Help: Assistance needed

  1. May 31, 2008 #1
    How many positive integers are multiples of 6 and factors of 180?

    I can find all factors of 180 and all multiples of 6 and compare, but that is not the mathematical way. I dont have a concrete idea how to start so any assistance would be more than enough.

    Thanx.
     
  2. jcsd
  3. May 31, 2008 #2
    Perhaps a "mathematical way" would be to consider the prime factorization, [itex]180 = 2^2 \cdot 3^2 \cdot 5 [/itex]. Therefore any factor of 180 which is a multiple of 6 is of the form [itex] 6 \cdot 2^a \cdot 3^b \cdot 5^c [/itex] where [itex] 0 \le a,b,c \le 1 [/itex]. Now it is easy to count how many possibilities there are.
     
  4. May 31, 2008 #3
    We know that the prime factors of 180 = 2*2*3*3*5.
    So, we can take (2*3) *2 = 6*2 =12 which is a multiple of 6 and a factor of 180.
    Next, take the prime factors 2*3 * 3 = 6*3 = 18. Thus, it is a multiple of 6 and a factor of 18.
    Continue, you see a pattern i.e. (2*3)*5, (2*3)*3*3... of permutations.
     
  5. May 31, 2008 #4

    tiny-tim

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    Hi Petkovsky! :smile:

    Hint: if 6n is a factor of 180,

    that means that 180/6n is a whole number,

    and so … ? :smile:
     
  6. Jun 1, 2008 #5
    Thank you :)
     
  7. Jun 1, 2008 #6

    tiny-tim

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    Physicsissuef, don't give the answer!

    (delete it if you still can)

    (i'm not sure it's right anyway …)

    Just give hints. :smile:
     
  8. Jun 1, 2008 #7
    6*2*3*5

    Yes, my answer wasn't correct actually :D

    6*2, 6*3, 6*5

    Maybe this is correct.
     
  9. Jun 1, 2008 #8

    tiny-tim

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    Physicsissuef, what part of "don't give the answer!" was not clear? :rolleyes:

    You know we're only supposed to give help, not complete answers!

    Well … you're obviously just guessing now … so no harm done! :smile:
     
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