1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Assistance needed
  1. Need a hint (Replies: 2)

Loading...